diff --git a/Lib/multiprocessing/pool.py b/Lib/multiprocessing/pool.py
index c66876a..bcbf7e3 100644
--- a/Lib/multiprocessing/pool.py
+++ b/Lib/multiprocessing/pool.py
@@ -294,7 +294,11 @@
 
     @staticmethod
     def _handle_workers(pool):
-        while pool._worker_handler._state == RUN and pool._state == RUN:
+        thread = threading.current_thread()
+
+        # Keep maintaining workers until the cache gets drained, unless the pool
+        # is terminated.
+        while thread._state == RUN or (pool._cache and thread._state != TERMINATE):
             pool._maintain_pool()
             time.sleep(0.1)
         # send sentinel to stop workers
diff --git a/Lib/test/test_multiprocessing.py b/Lib/test/test_multiprocessing.py
index 201fa98..14847d9 100644
--- a/Lib/test/test_multiprocessing.py
+++ b/Lib/test/test_multiprocessing.py
@@ -1168,6 +1168,20 @@
         p.close()
         p.join()
 
+    def test_pool_worker_lifetime_early_close(self):
+        # Issue #10332: closing a pool whose workers have limited lifetimes
+        # before all the tasks completed would make join() hang.
+        p = multiprocessing.Pool(3, maxtasksperchild=1)
+        results = []
+        for i in range(6):
+            results.append(p.apply_async(sqr, (i, 0.3)))
+        p.close()
+        p.join()
+        # check the results
+        for (j, res) in enumerate(results):
+            self.assertEqual(res.get(), sqr(j))
+
+
 #
 # Test that manager has expected number of shared objects left
 #
diff --git a/Misc/NEWS b/Misc/NEWS
index a501954..10daf5b 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -66,6 +66,9 @@
 Library
 -------
 
+- Issue #10332: multiprocessing: fix a race condition when a Pool is closed
+  before all tasks have completed.
+
 - Issue #1548891: The cStringIO.StringIO() constructor now encodes unicode
   arguments with the system default encoding just like the write() method
   does, instead of converting it to a raw buffer.  This also fixes handling of