diff --git a/haystack/core/errors.py b/haystack/core/errors.py
index 38cb2ce1a..3d750067d 100644
--- a/haystack/core/errors.py
+++ b/haystack/core/errors.py
@@ -10,9 +10,16 @@ class PipelineError(Exception):
 
 
 class PipelineRuntimeError(Exception):
-    def __init__(self, component_name: Optional[str], component_type: Optional[type], message: str) -> None:
+    def __init__(
+        self,
+        component_name: Optional[str],
+        component_type: Optional[type],
+        message: str,
+        pipeline_outputs: Optional[Any] = None,
+    ) -> None:
         self.component_name = component_name
         self.component_type = component_type
+        self.pipeline_outputs = pipeline_outputs
         super().__init__(message)
 
     @classmethod
diff --git a/haystack/core/pipeline/async_pipeline.py b/haystack/core/pipeline/async_pipeline.py
index dc5553b6d..70487e6a8 100644
--- a/haystack/core/pipeline/async_pipeline.py
+++ b/haystack/core/pipeline/async_pipeline.py
@@ -71,7 +71,12 @@ class AsyncPipeline(PipelineBase):
                 # Important: contextvars (e.g. active tracing Span) don’t propagate to running loop's ThreadPoolExecutor
                 # We use ctx.run(...) to preserve context like the active tracing span
                 ctx = contextvars.copy_context()
-                outputs = await loop.run_in_executor(None, lambda: ctx.run(lambda: instance.run(**component_inputs)))
+                try:
+                    outputs = await loop.run_in_executor(
+                        None, lambda: ctx.run(lambda: instance.run(**component_inputs))
+                    )
+                except Exception as error:
+                    raise PipelineRuntimeError.from_exception(component_name, instance.__class__, error) from error
 
             component_visits[component_name] += 1
 
@@ -256,13 +261,19 @@ class AsyncPipeline(PipelineBase):
                 )
                 component_inputs = self._consume_component_inputs(component_name, comp_dict, inputs_state)
                 component_inputs = self._add_missing_input_defaults(component_inputs, comp_dict["input_sockets"])
-                component_pipeline_outputs = await self._run_component_async(
-                    component_name=component_name,
-                    component=comp_dict,
-                    component_inputs=component_inputs,
-                    component_visits=component_visits,
-                    parent_span=parent_span,
-                )
+
+                try:
+                    component_pipeline_outputs = await self._run_component_async(
+                        component_name=component_name,
+                        component=comp_dict,
+                        component_inputs=component_inputs,
+                        component_visits=component_visits,
+                        parent_span=parent_span,
+                    )
+                except PipelineRuntimeError as error:
+                    # Attach partial pipeline outputs to the error before re-raising
+                    error.pipeline_outputs = pipeline_outputs
+                    raise error
 
                 # Distribute outputs to downstream inputs; also prune outputs based on `include_outputs_from`
                 pruned = self._write_component_outputs(
@@ -300,14 +311,19 @@ class AsyncPipeline(PipelineBase):
                 component_inputs = self._add_missing_input_defaults(component_inputs, comp_dict["input_sockets"])
 
                 async def _runner():
-                    async with ready_sem:
-                        component_pipeline_outputs = await self._run_component_async(
-                            component_name=component_name,
-                            component=comp_dict,
-                            component_inputs=component_inputs,
-                            component_visits=component_visits,
-                            parent_span=parent_span,
-                        )
+                    try:
+                        async with ready_sem:
+                            component_pipeline_outputs = await self._run_component_async(
+                                component_name=component_name,
+                                component=comp_dict,
+                                component_inputs=component_inputs,
+                                component_visits=component_visits,
+                                parent_span=parent_span,
+                            )
+                    except PipelineRuntimeError as error:
+                        # Attach partial pipeline outputs to the error before re-raising
+                        error.pipeline_outputs = pipeline_outputs
+                        raise error
 
                     # Distribute outputs to downstream inputs; also prune outputs based on `include_outputs_from`
                     pruned = self._write_component_outputs(
diff --git a/haystack/core/pipeline/breakpoint.py b/haystack/core/pipeline/breakpoint.py
index 22a604dae..410ccfcc5 100644
--- a/haystack/core/pipeline/breakpoint.py
+++ b/haystack/core/pipeline/breakpoint.py
@@ -163,10 +163,12 @@ def _save_pipeline_snapshot_to_file(
     if isinstance(pipeline_snapshot.break_point, AgentBreakpoint):
         agent_name = pipeline_snapshot.break_point.agent_name
         component_name = pipeline_snapshot.break_point.break_point.component_name
-        file_name = f"{agent_name}_{component_name}_{dt.strftime('%Y_%m_%d_%H_%M_%S')}.json"
+        visit_nr = pipeline_snapshot.pipeline_state.component_visits.get(component_name, 0)
+        file_name = f"{agent_name}_{component_name}_{visit_nr}_{dt.strftime('%Y_%m_%d_%H_%M_%S')}.json"
     else:
         component_name = pipeline_snapshot.break_point.component_name
-        file_name = f"{component_name}_{dt.strftime('%Y_%m_%d_%H_%M_%S')}.json"
+        visit_nr = pipeline_snapshot.pipeline_state.component_visits.get(component_name, 0)
+        file_name = f"{component_name}_{visit_nr}_{dt.strftime('%Y_%m_%d_%H_%M_%S')}.json"
 
     try:
         with open(snapshot_file_path / file_name, "w") as f_out:
diff --git a/haystack/core/pipeline/pipeline.py b/haystack/core/pipeline/pipeline.py
index d5301d2dd..0c6d97248 100644
--- a/haystack/core/pipeline/pipeline.py
+++ b/haystack/core/pipeline/pipeline.py
@@ -379,13 +379,18 @@ class Pipeline(PipelineBase):
                                 pipeline_snapshot=new_pipeline_snapshot, pipeline_outputs=pipeline_outputs
                             )
 
-                component_outputs = self._run_component(
-                    component_name=component_name,
-                    component=component,
-                    inputs=component_inputs,  # the inputs to the current component
-                    component_visits=component_visits,
-                    parent_span=span,
-                )
+                try:
+                    component_outputs = self._run_component(
+                        component_name=component_name,
+                        component=component,
+                        inputs=component_inputs,  # the inputs to the current component
+                        component_visits=component_visits,
+                        parent_span=span,
+                    )
+                except PipelineRuntimeError as error:
+                    # Attach partial pipeline outputs to the error before re-raising
+                    error.pipeline_outputs = pipeline_outputs
+                    raise error
 
                 # Updates global input state with component outputs and returns outputs that should go to
                 # pipeline outputs.
diff --git a/releasenotes/notes/handle-pipeline-crashes-and-resume-state-21c0e46a8935cbe2.yaml b/releasenotes/notes/handle-pipeline-crashes-and-resume-state-21c0e46a8935cbe2.yaml
new file mode 100644
index 000000000..6dd9ba84d
--- /dev/null
+++ b/releasenotes/notes/handle-pipeline-crashes-and-resume-state-21c0e46a8935cbe2.yaml
@@ -0,0 +1,6 @@
+---
+features:
+  - |
+    If an error occurs during the execution of a pipeline, the pipeline will raise an PipelineRuntimeError exception
+    containing an error message and the components outputs up to the point of failure. This allows you to inspect and
+    debug the pipeline up to the point of failure.
diff --git a/test/core/pipeline/test_pipeline_crash_regular_pipeline_outputs_raised.py b/test/core/pipeline/test_pipeline_crash_regular_pipeline_outputs_raised.py
new file mode 100644
index 000000000..688b55046
--- /dev/null
+++ b/test/core/pipeline/test_pipeline_crash_regular_pipeline_outputs_raised.py
@@ -0,0 +1,234 @@
+# SPDX-FileCopyrightText: 2022-present deepset GmbH <info@deepset.ai>
+#
+# SPDX-License-Identifier: Apache-2.0
+
+from unittest.mock import MagicMock, patch
+
+import numpy as np
+import pytest
+
+from haystack import AsyncPipeline, Document, Pipeline
+from haystack.components.builders import ChatPromptBuilder
+from haystack.components.builders.answer_builder import AnswerBuilder
+from haystack.components.embedders import SentenceTransformersTextEmbedder
+from haystack.components.generators.chat import OpenAIChatGenerator
+from haystack.components.joiners import DocumentJoiner
+from haystack.components.retrievers.in_memory import InMemoryBM25Retriever
+from haystack.components.writers import DocumentWriter
+from haystack.core.component import component
+from haystack.core.errors import PipelineRuntimeError
+from haystack.dataclasses import ChatMessage
+from haystack.document_stores.in_memory import InMemoryDocumentStore
+from haystack.document_stores.types import DuplicatePolicy
+from haystack.utils.auth import Secret
+
+
+def setup_document_store():
+    """Create and populate a document store with test documents."""
+    documents = [
+        Document(content="My name is Jean and I live in Paris.", embedding=[0.1, 0.3, 0.6]),
+        Document(content="My name is Mark and I live in Berlin.", embedding=[0.2, 0.4, 0.7]),
+        Document(content="My name is Giorgio and I live in Rome.", embedding=[0.3, 0.5, 0.8]),
+    ]
+
+    document_store = InMemoryDocumentStore()
+    doc_writer = DocumentWriter(document_store=document_store, policy=DuplicatePolicy.SKIP)
+    doc_writer.run(documents=documents)
+
+    return document_store
+
+
+# Create a mock component that returns invalid output (int instead of documents list)
+@component
+class InvalidOutputEmbeddingRetriever:
+    @component.output_types(documents=list[Document])
+    def run(self, query_embedding: list[float]):
+        # Return an int instead of the expected documents list
+        # This will cause the pipeline to crash when trying to pass it to the next component
+        return 42
+
+
+template = [
+    ChatMessage.from_system(
+        "You are a helpful AI assistant. Answer the following question based on the given context information "
+        "only. If the context is empty or just a '\n' answer with None, example: 'None'."
+    ),
+    ChatMessage.from_user(
+        """
+        Context:
+        {% for document in documents %}
+            {{ document.content }}
+        {% endfor %}
+
+        Question: {{question}}
+        """
+    ),
+]
+
+
+class TestPipelineOutputsRaisedInException:
+    @pytest.fixture
+    def mock_sentence_transformers_text_embedder(self):
+        with patch(
+            "haystack.components.embedders.sentence_transformers_text_embedder._SentenceTransformersEmbeddingBackendFactory"
+        ) as mock_text_embedder:
+            mock_model = MagicMock()
+            mock_text_embedder.return_value = mock_model
+
+            def mock_encode(
+                texts, batch_size=None, show_progress_bar=None, normalize_embeddings=None, precision=None, **kwargs
+            ):  # noqa E501
+                return [np.ones(384).tolist() for _ in texts]
+
+            mock_model.encode = mock_encode
+            embedder = SentenceTransformersTextEmbedder(model="mock-model", progress_bar=False)
+
+            def mock_run(text):
+                if not isinstance(text, str):
+                    raise TypeError(
+                        "SentenceTransformersTextEmbedder expects a string as input."
+                        "In case you want to embed a list of Documents, please use the "
+                        "SentenceTransformersDocumentEmbedder."
+                    )
+
+                embedding = np.ones(384).tolist()
+                return {"embedding": embedding}
+
+            embedder.run = mock_run
+            embedder.warm_up()
+            return embedder
+
+    def test_hybrid_rag_pipeline_crash_on_embedding_retriever(
+        self, mock_sentence_transformers_text_embedder, monkeypatch
+    ):
+        monkeypatch.setenv("OPENAI_API_KEY", "test-api-key")
+
+        document_store = setup_document_store()
+        text_embedder = mock_sentence_transformers_text_embedder
+        invalid_embedding_retriever = InvalidOutputEmbeddingRetriever()
+        bm25_retriever = InMemoryBM25Retriever(document_store)
+        document_joiner = DocumentJoiner(join_mode="concatenate")
+
+        pipeline = Pipeline()
+        pipeline.add_component("text_embedder", text_embedder)
+        pipeline.add_component("embedding_retriever", invalid_embedding_retriever)
+        pipeline.add_component("bm25_retriever", bm25_retriever)
+        pipeline.add_component("document_joiner", document_joiner)
+        pipeline.add_component(
+            "prompt_builder", ChatPromptBuilder(template=template, required_variables=["question", "documents"])
+        )
+        pipeline.add_component("llm", OpenAIChatGenerator(api_key=Secret.from_env_var("OPENAI_API_KEY")))
+        pipeline.add_component("answer_builder", AnswerBuilder())
+
+        pipeline.connect("text_embedder", "embedding_retriever")
+        pipeline.connect("bm25_retriever", "document_joiner")
+        pipeline.connect("embedding_retriever", "document_joiner")
+        pipeline.connect("document_joiner.documents", "prompt_builder.documents")
+        pipeline.connect("prompt_builder", "llm")
+        pipeline.connect("llm.replies", "answer_builder.replies")
+
+        question = "Where does Mark live?"
+        test_data = {
+            "text_embedder": {"text": question},
+            "bm25_retriever": {"query": question},
+            "prompt_builder": {"question": question},
+            "answer_builder": {"query": question},
+        }
+
+        # run pipeline and expect it to crash due to invalid output type
+        with pytest.raises(PipelineRuntimeError) as exc_info:
+            pipeline.run(
+                data=test_data,
+                include_outputs_from={
+                    "text_embedder",
+                    "embedding_retriever",
+                    "bm25_retriever",
+                    "document_joiner",
+                    "prompt_builder",
+                    "llm",
+                    "answer_builder",
+                },
+            )
+
+        pipeline_outputs = exc_info.value.pipeline_outputs
+
+        assert pipeline_outputs is not None, "Pipeline outputs should be captured in the exception"
+
+        # verify that bm25_retriever and text_embedder ran successfully before the crash
+        assert "bm25_retriever" in pipeline_outputs, "BM25 retriever output not captured"
+        assert "documents" in pipeline_outputs["bm25_retriever"], "BM25 retriever should have produced documents"
+        assert "text_embedder" in pipeline_outputs, "Text embedder output not captured"
+        assert "embedding" in pipeline_outputs["text_embedder"], "Text embedder should have produced embeddings"
+
+        # components after the crash point are not in the outputs
+        assert "document_joiner" not in pipeline_outputs, "Document joiner should not have run due to crash"
+        assert "prompt_builder" not in pipeline_outputs, "Prompt builder should not have run due to crash"
+        assert "llm" not in pipeline_outputs, "LLM should not have run due to crash"
+        assert "answer_builder" not in pipeline_outputs, "Answer builder should not have run due to crash"
+
+    @pytest.mark.asyncio
+    async def test_async_hybrid_rag_pipeline_crash_on_embedding_retriever(
+        self, mock_sentence_transformers_text_embedder, monkeypatch
+    ):
+        monkeypatch.setenv("OPENAI_API_KEY", "test-api-key")
+
+        document_store = setup_document_store()
+        text_embedder = mock_sentence_transformers_text_embedder
+        invalid_embedding_retriever = InvalidOutputEmbeddingRetriever()
+        bm25_retriever = InMemoryBM25Retriever(document_store)
+        document_joiner = DocumentJoiner(join_mode="concatenate")
+
+        pipeline = AsyncPipeline()
+        pipeline.add_component("text_embedder", text_embedder)
+        pipeline.add_component("embedding_retriever", invalid_embedding_retriever)
+        pipeline.add_component("bm25_retriever", bm25_retriever)
+        pipeline.add_component("document_joiner", document_joiner)
+        pipeline.add_component(
+            "prompt_builder", ChatPromptBuilder(template=template, required_variables=["question", "documents"])
+        )
+        pipeline.add_component("llm", OpenAIChatGenerator(api_key=Secret.from_env_var("OPENAI_API_KEY")))
+        pipeline.add_component("answer_builder", AnswerBuilder())
+
+        pipeline.connect("text_embedder", "embedding_retriever")
+        pipeline.connect("bm25_retriever", "document_joiner")
+        pipeline.connect("embedding_retriever", "document_joiner")
+        pipeline.connect("document_joiner.documents", "prompt_builder.documents")
+        pipeline.connect("prompt_builder", "llm")
+        pipeline.connect("llm.replies", "answer_builder.replies")
+
+        question = "Where does Mark live?"
+        test_data = {
+            "text_embedder": {"text": question},
+            "bm25_retriever": {"query": question},
+            "prompt_builder": {"question": question},
+            "answer_builder": {"query": question},
+        }
+
+        with pytest.raises(PipelineRuntimeError) as exc_info:
+            await pipeline.run_async(
+                data=test_data,
+                include_outputs_from={
+                    "text_embedder",
+                    "embedding_retriever",
+                    "bm25_retriever",
+                    "document_joiner",
+                    "prompt_builder",
+                    "llm",
+                    "answer_builder",
+                },
+            )
+
+        pipeline_outputs = exc_info.value.pipeline_outputs
+        assert pipeline_outputs is not None, "Pipeline outputs should be captured in the exception"
+
+        # verify that bm25_retriever and text_embedder ran successfully before the crash
+        assert "bm25_retriever" in pipeline_outputs, "BM25 retriever output not captured"
+        assert "documents" in pipeline_outputs["bm25_retriever"], "BM25 retriever should have produced documents"
+        assert "text_embedder" in pipeline_outputs, "Text embedder output not captured"
+        assert "embedding" in pipeline_outputs["text_embedder"], "Text embedder should have produced embeddings"
+
+        # components after the crash point are not in the outputs
+        assert "document_joiner" not in pipeline_outputs, "Document joiner should not have run due to crash"
+        assert "prompt_builder" not in pipeline_outputs, "Prompt builder should not have run due to crash"
+        assert "llm" not in pipeline_outputs, "LLM should not have run due to crash"
+        assert "answer_builder" not in pipeline_outputs, "Answer builder should not have run due to crash"