diff --git a/Lib/concurrent/futures/process.py b/Lib/concurrent/futures/process.py
index 301207f59de..9933d3d0e04 100644
--- a/Lib/concurrent/futures/process.py
+++ b/Lib/concurrent/futures/process.py
@@ -489,7 +489,14 @@ class _ExecutorManagerThread(threading.Thread):
 
         # Mark pending tasks as failed.
         for work_id, work_item in self.pending_work_items.items():
-            work_item.future.set_exception(bpe)
+            try:
+                work_item.future.set_exception(bpe)
+            except _base.InvalidStateError as exc:
+                # set_exception() fails if the future is cancelled: ignore it.
+                # Trying to check if the future is cancelled before calling
+                # set_exception() would leave a race condition if the future is
+                # cancelled betwen the check and set_exception().
+                pass
             # Delete references to object. See issue16284
             del work_item
         self.pending_work_items.clear()
diff --git a/Lib/test/test_concurrent_futures/test_deadlock.py b/Lib/test/test_concurrent_futures/test_deadlock.py
index 6b78b360d15..baac2b51e0d 100644
--- a/Lib/test/test_concurrent_futures/test_deadlock.py
+++ b/Lib/test/test_concurrent_futures/test_deadlock.py
@@ -239,6 +239,8 @@ class ExecutorDeadlockTest:
             with self.assertRaises(BrokenProcessPool):
                 list(executor.map(_crash_with_data, [data] * 10))
 
+        executor.shutdown(wait=True)
+
 
 create_executor_tests(globals(), ExecutorDeadlockTest,
                       executor_mixins=(ProcessPoolForkMixin,