diff --git a/Lib/test/test_threading.py b/Lib/test/test_threading.py
index c7a2213..1e1e625 100644
--- a/Lib/test/test_threading.py
+++ b/Lib/test/test_threading.py
@@ -286,6 +286,29 @@
         self.assertFalse(rc == 2, "interpreted was blocked")
         self.assertTrue(rc == 0, "Unexpected error")
 
+    def test_join_nondaemon_on_shutdown(self):
+        # Issue 1722344
+        # Raising SystemExit skipped threading._shutdown
+        import subprocess
+        p = subprocess.Popen([sys.executable, "-c", """if 1:
+                import threading
+                from time import sleep
+
+                def child():
+                    sleep(1)
+                    # As a non-daemon thread we SHOULD wake up and nothing
+                    # should be torn down yet
+                    print("Woke up, sleep function is:", sleep)
+
+                threading.Thread(target=child).start()
+                raise SystemExit
+            """],
+            stdout=subprocess.PIPE,
+            stderr=subprocess.PIPE)
+        stdout, stderr = p.communicate()
+        self.assertEqual(stdout, b"Woke up, sleep function is: <built-in function sleep>\n")
+        stderr = re.sub(br"^\[\d+ refs\]", b"", stderr, re.MULTILINE).strip()
+        self.assertEqual(stderr, b"")
 
     def test_enumerate_after_join(self):
         # Try hard to trigger #1703448: a thread is still returned in