diff --git a/haystack/core/pipeline/pipeline.py b/haystack/core/pipeline/pipeline.py
index 10d0389a3..498daa5c9 100644
--- a/haystack/core/pipeline/pipeline.py
+++ b/haystack/core/pipeline/pipeline.py
@@ -897,12 +897,15 @@ class Pipeline:
                         and last_waiting_for_input is not None
                         and before_last_waiting_for_input == last_waiting_for_input
                     ):
-                        # Are we actually stuck or there's a lazy variadic waiting for input?
-                        # This is our last resort, if there's no lazy variadic waiting for input
+                        # Are we actually stuck or there's a lazy variadic or a component with has only default inputs waiting for input?
+                        # This is our last resort, if there's no lazy variadic or component with only default inputs waiting for input
                         # we're stuck for real and we can't make any progress.
                         for name, comp in waiting_for_input:
                             is_variadic = any(socket.is_variadic for socket in comp.__haystack_input__._sockets_dict.values())  # type: ignore
-                            if is_variadic and not comp.__haystack_is_greedy__:  # type: ignore[attr-defined]
+                            has_only_defaults = all(
+                                not socket.is_mandatory for socket in comp.__haystack_input__._sockets_dict.values()  # type: ignore
+                            )
+                            if is_variadic and not comp.__haystack_is_greedy__ or has_only_defaults:  # type: ignore[attr-defined]
                                 break
                         else:
                             # We're stuck in a loop for real, we can't make any progress.
@@ -910,13 +913,13 @@ class Pipeline:
                             break
 
                         if len(waiting_for_input) == 1:
-                            # We have a single component with variadic input waiting for input.
+                            # We have a single component with variadic input or only default inputs waiting for input.
                             # If we're at this point it means it has been waiting for input for at least 2 iterations.
                             # This will never run.
                             # BAIL!
                             break
 
-                        # There was a lazy variadic waiting for input, we can run it
+                        # There was a lazy variadic or a component with only default waiting for input, we can run it
                         waiting_for_input.remove((name, comp))
                         to_run.append((name, comp))
                         continue
diff --git a/test/core/pipeline/test_pipeline.py b/test/core/pipeline/test_pipeline.py
index ab493b9c6..18bfe63b0 100644
--- a/test/core/pipeline/test_pipeline.py
+++ b/test/core/pipeline/test_pipeline.py
@@ -9,6 +9,7 @@ import pytest
 
 from haystack import Document
 from haystack.components.builders import PromptBuilder
+from haystack.components.builders.answer_builder import AnswerBuilder
 from haystack.components.others import Multiplexer
 from haystack.components.retrievers.in_memory import InMemoryBM25Retriever
 from haystack.core.component import component
@@ -807,3 +808,39 @@ def test_correct_execution_order_of_components_with_only_defaults(spying_tracer)
             "Question: What is the capital of France?"
         }
     }
+
+
+def test_pipeline_is_not_stuck_with_components_with_only_defaults():
+    FakeGenerator = component_class(
+        "FakeGenerator", input_types={"prompt": str}, output_types={"replies": List[str]}, output={"replies": ["Paris"]}
+    )
+    docs = [Document(content="Rome is the capital of Italy"), Document(content="Paris is the capital of France")]
+    doc_store = InMemoryDocumentStore()
+    doc_store.write_documents(docs)
+    template = (
+        "Given the following information, answer the question.\n"
+        "Context:\n"
+        "{% for document in documents %}"
+        "    {{ document.content }}\n"
+        "{% endfor %}"
+        "Question: {{ query }}"
+    )
+
+    pipe = Pipeline()
+
+    pipe.add_component("retriever", InMemoryBM25Retriever(document_store=doc_store))
+    pipe.add_component("prompt_builder", PromptBuilder(template=template))
+    pipe.add_component("generator", FakeGenerator())
+    pipe.add_component("answer_builder", AnswerBuilder())
+
+    pipe.connect("retriever", "prompt_builder.documents")
+    pipe.connect("prompt_builder.prompt", "generator.prompt")
+    pipe.connect("generator.replies", "answer_builder.replies")
+    pipe.connect("retriever.documents", "answer_builder.documents")
+
+    query = "What is the capital of France?"
+    res = pipe.run({"query": query})
+    assert len(res) == 1
+    answers = res["answer_builder"]["answers"]
+    assert len(answers) == 1
+    assert answers[0].data == "Paris"