diff --git a/Lib/test/test_threading.py b/Lib/test/test_threading.py
index 6ac4ea9..ad90010 100644
--- a/Lib/test/test_threading.py
+++ b/Lib/test/test_threading.py
@@ -583,6 +583,41 @@
         self.assertEqual(data.splitlines(),
                          ["GC: True True True"] * 2)
 
+    def test_finalization_shutdown(self):
+        # bpo-36402: Py_Finalize() calls threading._shutdown() which must wait
+        # until Python thread states of all non-daemon threads get deleted.
+        #
+        # Test similar to SubinterpThreadingTests.test_threads_join_2(), but
+        # test the finalization of the main interpreter.
+        code = """if 1:
+            import os
+            import threading
+            import time
+            import random
+
+            def random_sleep():
+                seconds = random.random() * 0.010
+                time.sleep(seconds)
+
+            class Sleeper:
+                def __del__(self):
+                    random_sleep()
+
+            tls = threading.local()
+
+            def f():
+                # Sleep a bit so that the thread is still running when
+                # Py_Finalize() is called.
+                random_sleep()
+                tls.x = Sleeper()
+                random_sleep()
+
+            threading.Thread(target=f).start()
+            random_sleep()
+        """
+        rc, out, err = assert_python_ok("-c", code)
+        self.assertEqual(err, b"")
+
     def test_tstate_lock(self):
         # Test an implementation detail of Thread objects.
         started = _thread.allocate_lock()
@@ -878,15 +913,22 @@
         self.addCleanup(os.close, w)
         code = r"""if 1:
             import os
+            import random
             import threading
             import time
 
+            def random_sleep():
+                seconds = random.random() * 0.010
+                time.sleep(seconds)
+
             def f():
                 # Sleep a bit so that the thread is still running when
                 # Py_EndInterpreter is called.
-                time.sleep(0.05)
+                random_sleep()
                 os.write(%d, b"x")
+
             threading.Thread(target=f).start()
+            random_sleep()
             """ % (w,)
         ret = test.support.run_in_subinterp(code)
         self.assertEqual(ret, 0)
@@ -903,22 +945,29 @@
         self.addCleanup(os.close, w)
         code = r"""if 1:
             import os
+            import random
             import threading
             import time
 
+            def random_sleep():
+                seconds = random.random() * 0.010
+                time.sleep(seconds)
+
             class Sleeper:
                 def __del__(self):
-                    time.sleep(0.05)
+                    random_sleep()
 
             tls = threading.local()
 
             def f():
                 # Sleep a bit so that the thread is still running when
                 # Py_EndInterpreter is called.
-                time.sleep(0.05)
+                random_sleep()
                 tls.x = Sleeper()
                 os.write(%d, b"x")
+
             threading.Thread(target=f).start()
+            random_sleep()
             """ % (w,)
         ret = test.support.run_in_subinterp(code)
         self.assertEqual(ret, 0)
diff --git a/Lib/threading.py b/Lib/threading.py
index 3d197ee..6792640 100644
--- a/Lib/threading.py
+++ b/Lib/threading.py
@@ -739,6 +739,11 @@
 _active = {}    # maps thread id to Thread object
 _limbo = {}
 _dangling = WeakSet()
+# Set of Thread._tstate_lock locks of non-daemon threads used by _shutdown()
+# to wait until all Python thread states get deleted:
+# see Thread._set_tstate_lock().
+_shutdown_locks_lock = _allocate_lock()
+_shutdown_locks = set()
 
 # Main class for threads
 
@@ -903,6 +908,10 @@
         self._tstate_lock = _set_sentinel()
         self._tstate_lock.acquire()
 
+        if not self.daemon:
+            with _shutdown_locks_lock:
+                _shutdown_locks.add(self._tstate_lock)
+
     def _bootstrap_inner(self):
         try:
             self._set_ident()
@@ -954,6 +963,9 @@
             assert not lock.locked()
         self._is_stopped = True
         self._tstate_lock = None
+        if not self.daemon:
+            with _shutdown_locks_lock:
+                _shutdown_locks.discard(self._tstate_lock)
 
     def _delete(self):
         "Remove current thread from the dict of currently running threads."
@@ -1342,6 +1354,9 @@
 _main_thread = _MainThread()
 
 def _shutdown():
+    """
+    Wait until the Python thread state of all non-daemon threads get deleted.
+    """
     # Obscure:  other threads may be waiting to join _main_thread.  That's
     # dubious, but some code does it.  We can't wait for C code to release
     # the main thread's tstate_lock - that won't happen until the interpreter
@@ -1350,6 +1365,8 @@
     if _main_thread._is_stopped:
         # _shutdown() was already called
         return
+
+    # Main thread
     tlock = _main_thread._tstate_lock
     # The main thread isn't finished yet, so its thread state lock can't have
     # been released.
@@ -1357,16 +1374,24 @@
     assert tlock.locked()
     tlock.release()
     _main_thread._stop()
-    t = _pickSomeNonDaemonThread()
-    while t:
-        t.join()
-        t = _pickSomeNonDaemonThread()
 
-def _pickSomeNonDaemonThread():
-    for t in enumerate():
-        if not t.daemon and t.is_alive():
-            return t
-    return None
+    # Join all non-deamon threads
+    while True:
+        with _shutdown_locks_lock:
+            locks = list(_shutdown_locks)
+            _shutdown_locks.clear()
+
+        if not locks:
+            break
+
+        for lock in locks:
+            # mimick Thread.join()
+            lock.acquire()
+            lock.release()
+
+        # new threads can be spawned while we were waiting for the other
+        # threads to complete
+
 
 def main_thread():
     """Return the main thread object.
@@ -1392,12 +1417,18 @@
     # Reset _active_limbo_lock, in case we forked while the lock was held
     # by another (non-forked) thread.  http://bugs.python.org/issue874900
     global _active_limbo_lock, _main_thread
+    global _shutdown_locks_lock, _shutdown_locks
     _active_limbo_lock = _allocate_lock()
 
     # fork() only copied the current thread; clear references to others.
     new_active = {}
     current = current_thread()
     _main_thread = current
+
+    # reset _shutdown() locks: threads re-register their _tstate_lock below
+    _shutdown_locks_lock = _allocate_lock()
+    _shutdown_locks = set()
+
     with _active_limbo_lock:
         # Dangling thread instances must still have their locks reset,
         # because someone may join() them.
diff --git a/Misc/NEWS.d/next/Library/2019-06-11-00-35-02.bpo-36402.b0IJVp.rst b/Misc/NEWS.d/next/Library/2019-06-11-00-35-02.bpo-36402.b0IJVp.rst
new file mode 100644
index 0000000..3bc537e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-06-11-00-35-02.bpo-36402.b0IJVp.rst
@@ -0,0 +1,4 @@
+Fix a race condition at Python shutdown when waiting for threads. Wait until
+the Python thread state of all non-daemon threads get deleted (join all
+non-daemon threads), rather than just wait until non-daemon Python threads
+complete.