diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3d7de53a..97cd88f7 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,9 @@ releases are available on [PyPI](https://pypi.org/project/pytask) and
 
 ## Unreleased
 
+- [#936](https://github.com/pytask-dev/pytask/pull/936) runs tasks without paths when
+  their source cannot be inspected, while still rejecting path-backed tasks with
+  missing source files.
 - [#997](https://github.com/pytask-dev/pytask/pull/997) documents how task generators
   behave in dry-run and explain modes and adds regression tests for both modes.
 - [#995](https://github.com/pytask-dev/pytask/pull/995) documents that return values
diff --git a/src/_pytask/execute.py b/src/_pytask/execute.py
index 81f530d5..266e153b 100644
--- a/src/_pytask/execute.py
+++ b/src/_pytask/execute.py
@@ -33,6 +33,7 @@
 from _pytask.node_protocols import PPathNode
 from _pytask.node_protocols import PProvisionalNode
 from _pytask.node_protocols import PTask
+from _pytask.node_protocols import PTaskWithPath
 from _pytask.nodes import DirectoryNode
 from _pytask.outcomes import Exit
 from _pytask.outcomes import SkippedUnchanged
@@ -172,7 +173,7 @@ def pytask_execute_task_setup(session: Session, task: PTask) -> None:  # noqa: C
         )
 
     if not needs_to_be_executed:
-        predecessors = set(dag.predecessors(task.signature)) | {task.signature}
+        predecessors = set(dag.predecessors(task.signature))
         for node_signature in node_and_neighbors(dag, task.signature):
             node = dag.nodes[node_signature]
 
@@ -192,7 +193,11 @@ def pytask_execute_task_setup(session: Session, task: PTask) -> None:  # noqa: C
 
             node_state = node.state()
 
-            if node_signature in predecessors and not node_state:
+            # Dependencies and source files must exist; sourceless tasks may lack state.
+            is_required = node_signature in predecessors or (
+                node_signature == task.signature and isinstance(task, PTaskWithPath)
+            )
+            if is_required and not node_state:
                 msg = f"{task.name!r} requires missing node {node.name!r}."
                 if IS_FILE_SYSTEM_CASE_SENSITIVE:
                     msg += (
diff --git a/tests/test_execute.py b/tests/test_execute.py
index 5067d6ac..6ccc4f41 100644
--- a/tests/test_execute.py
+++ b/tests/test_execute.py
@@ -18,6 +18,7 @@
 from pytask import ExitCode
 from pytask import NodeNotFoundError
 from pytask import PathNode
+from pytask import Task
 from pytask import TaskOutcome
 from pytask import TaskWithoutPath
 from pytask import build
@@ -967,6 +968,56 @@ def func(path):
     assert session.exit_code == ExitCode.OK
 
 
+def test_sourceless_task_without_path_always_executes(tmp_path):
+    namespace = {}
+    exec(  # noqa: S102
+        textwrap.dedent(
+            """
+            def function(path):
+                count = int(path.read_text()) if path.exists() else 0
+                path.write_text(str(count + 1))
+            """
+        ),
+        namespace,
+    )
+    task = TaskWithoutPath(
+        name="sourceless",
+        function=namespace["function"],
+        produces={"path": PathNode(path=tmp_path / "count.txt")},
+    )
+
+    assert task.state() is None
+
+    first_session = build(tasks=task, paths=tmp_path)
+    second_session = build(tasks=task, paths=tmp_path)
+
+    assert first_session.exit_code == ExitCode.OK
+    assert second_session.exit_code == ExitCode.OK
+    assert tmp_path.joinpath("count.txt").read_text() == "2"
+    assert first_session.execution_reports[0].outcome == TaskOutcome.SUCCESS
+    assert second_session.execution_reports[0].outcome == TaskOutcome.SUCCESS
+
+
+def test_task_with_missing_source_fails(tmp_path):
+    output_path = tmp_path / "out.txt"
+    task = Task(
+        base_name="task",
+        path=tmp_path / "missing.py",
+        function=lambda path: path.touch(),
+        produces={"path": PathNode(path=output_path)},
+    )
+
+    session = build(tasks=task, paths=tmp_path)
+
+    assert session.exit_code == ExitCode.FAILED
+    assert not output_path.exists()
+    report = session.execution_reports[0]
+    assert report.outcome == TaskOutcome.FAIL
+    exc_info = report.exc_info
+    assert exc_info is not None
+    assert isinstance(exc_info[1], NodeNotFoundError)
+
+
 def test_collect_task(runner, tmp_path):
     source = """
     from pytask import Task, PathNode