Add unit test

Closes: #49451
Signed-off-by: Chi-Sheng Liu <[email protected]>

python/ray/tests/test_actor_failures.py

@@ -989,6 +989,39 @@ def verify():
     wait_for_condition(verify)
 
 
+def test_exit_actor_async_actor_nested_task(shutdown_only, tmp_path):
+    async_temp_file = tmp_path / "async_actor.log"
+    async_temp_file.touch()
+
+    @ray.remote
+    class AsyncActor:
+        def __init__(self):
+            def f():
+                print("atexit handler")
+                with open(async_temp_file, "w") as f:
+                    f.write("Async Actor\n")
+
+            atexit.register(f)
+
+        async def start_exit_task(self):
+            asyncio.create_task(self.exit())
+
+        async def exit(self):
+            exit_actor()
+
+    a = AsyncActor.remote()
+    ray.get(a.__ray_ready__.remote())
+    with pytest.raises(ray.exceptions.RayActorError):
+        ray.get(a.start_exit_task.remote())
+
+    def verify():
+        with open(async_temp_file) as f:
+            assert f.readlines() == ["Async Actor\n"]
+        return True
+
+    wait_for_condition(verify)
+
+
 def test_exit_actor_queued(shutdown_only):
     """Verify after exit_actor is called the queued tasks won't execute."""