diff --git a/Lib/multiprocessing/pool.py b/Lib/multiprocessing/pool.py
index b223d6aa724bb6..41dd923d4f9740 100644
--- a/Lib/multiprocessing/pool.py
+++ b/Lib/multiprocessing/pool.py
@@ -651,8 +651,6 @@ def close(self):
     def terminate(self):
         util.debug('terminating pool')
         self._state = TERMINATE
-        self._worker_handler._state = TERMINATE
-        self._change_notifier.put(None)
         self._terminate()
 
     def join(self):
@@ -682,7 +680,12 @@ def _terminate_pool(cls, taskqueue, inqueue, outqueue, pool, change_notifier,
         # this is guaranteed to only be called once
         util.debug('finalizing pool')
 
+        # Notify that the worker_handler state has been changed so the
+        # _handle_workers loop can be unblocked (and exited) in order to
+        # send the finalization sentinel all the workers.
         worker_handler._state = TERMINATE
+        change_notifier.put(None)
+
         task_handler._state = TERMINATE
 
         util.debug('helping task handler/workers to finish')
diff --git a/Lib/test/_test_multiprocessing.py b/Lib/test/_test_multiprocessing.py
index b985d51508cb75..4a87b1761f9efe 100644
--- a/Lib/test/_test_multiprocessing.py
+++ b/Lib/test/_test_multiprocessing.py
@@ -2780,6 +2780,24 @@ def test_pool_worker_lifetime_early_close(self):
         for (j, res) in enumerate(results):
             self.assertEqual(res.get(), sqr(j))
 
+    def test_worker_finalization_via_atexit_handler_of_multiprocessing(self):
+        # tests cases against bpo-38744 and bpo-39360
+        cmd = '''if 1:
+            from multiprocessing import Pool
+            problem = None
+            class A:
+                def __init__(self):
+                    self.pool = Pool(processes=1)
+            def test():
+                global problem
+                problem = A()
+                problem.pool.map(float, tuple(range(10)))
+            if __name__ == "__main__":
+                test()
+        '''
+        rc, out, err = test.support.script_helper.assert_python_ok('-c', cmd)
+        self.assertEqual(rc, 0)
+
 #
 # Test of creating a customized manager class
 #
diff --git a/Misc/NEWS.d/next/Library/2020-03-15-05-41-05.bpo-39360.cmcU5p.rst b/Misc/NEWS.d/next/Library/2020-03-15-05-41-05.bpo-39360.cmcU5p.rst
new file mode 100644
index 00000000000000..148878886e6ee5
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-03-15-05-41-05.bpo-39360.cmcU5p.rst
@@ -0,0 +1,4 @@
+Ensure all workers exit when finalizing a :class:`multiprocessing.Pool` implicitly via the module finalization
+handlers of multiprocessing. This fixes a deadlock situation that can be experienced when the Pool is not
+properly finalized via the context manager or a call to ``multiprocessing.Pool.terminate``. Patch by Batuhan Taskaya
+and Pablo Galindo.