diff --git a/distributed/tests/test_worker_memory.py b/distributed/tests/test_worker_memory.py
index 7698a2bddc2..e385ca07b34 100644
--- a/distributed/tests/test_worker_memory.py
+++ b/distributed/tests/test_worker_memory.py
@@ -480,6 +480,73 @@ def f(ev):
         assert "Resuming worker" in logger.getvalue()
 
 
+@gen_cluster(
+    client=True,
+    nthreads=[("", 1), ("", 1)],
+    config={
+        "distributed.worker.memory.target": False,
+        "distributed.worker.memory.spill": False,
+        "distributed.worker.memory.pause": False,
+    },
+)
+async def test_pause_prevents_deps_fetch(c, s, a, b):
+    """A worker is paused while there are dependencies ready to fetch, but all other
+    workers are in flight
+    """
+    a_addr = a.address
+
+    class X:
+        def __sizeof__(self):
+            return 2**40  # Disable clustering in select_keys_for_gather
+
+        def __reduce__(self):
+            return X.pause_on_unpickle, ()
+
+        @staticmethod
+        def pause_on_unpickle():
+            # Note: outside of task execution, distributed.get_worker()
+            # returns a random worker running in the process
+            for w in Worker._instances:
+                if w.address == a_addr:
+                    w.status = Status.paused
+                    return X()
+            assert False
+
+    x = c.submit(X, key="x", workers=[b.address])
+    y = c.submit(inc, 1, key="y", workers=[b.address])
+    await wait([x, y])
+    w = c.submit(lambda _: None, x, key="w", priority=1, workers=[a.address])
+    z = c.submit(inc, y, key="z", priority=0, workers=[a.address])
+
+    # - w and z reach worker a within the same message
+    # - w and z respectively make x and y go into fetch state.
+    #   w has a higher priority than z, therefore w's dependency x has a higher priority
+    #   than z's dependency y.
+    #   a.data_needed = ["x", "y"]
+    # - ensure_communicating decides to fetch x but not to fetch y together with it, as
+    #   it thinks x is 1TB in size
+    # - x fetch->flight; a is added to in_flight_workers
+    # - y is skipped by ensure_communicating since all workers that hold a replica are
+    #   in flight
+    # - x reaches a and sends a into paused state
+    # - x flight->memory; a is removed from in_flight_workers
+    # - ensure_communicating is triggered again
+    # - ensure_communicating refuses to fetch y because the worker is paused
+
+    while "y" not in a.tasks or a.tasks["y"].state != "fetch":
+        await asyncio.sleep(0.01)
+    await asyncio.sleep(0.1)
+    assert a.tasks["y"].state == "fetch"
+    assert "y" not in a.data
+    assert [ts.key for ts in a.data_needed] == ["y"]
+
+    # Unpausing kicks off ensure_communicating again
+    a.status = Status.running
+    assert await z == 3
+    assert a.tasks["y"].state == "memory"
+    assert "y" in a.data
+
+
 @gen_cluster(
     client=True,
     nthreads=[("", 1)],
diff --git a/distributed/worker.py b/distributed/worker.py
index 6475fea0930..e5563ed09d7 100644
--- a/distributed/worker.py
+++ b/distributed/worker.py
@@ -2748,6 +2748,9 @@ def stimulus_story(
         return [ev for ev in self.stimulus_log if getattr(ev, "key", None) in keys]
 
     def ensure_communicating(self) -> None:
+        if self.status != Status.running:
+            return
+
         stimulus_id = f"ensure-communicating-{time()}"
         skipped_worker_in_flight_or_busy = []
 
@@ -3489,7 +3492,7 @@ async def _maybe_deserialize_task(
             raise
 
     def _ensure_computing(self) -> RecsInstrs:
-        if self.status in (Status.paused, Status.closing_gracefully):
+        if self.status != Status.running:
             return {}, []
 
         recs: Recs = {}