In the Pool class, when the pool is terminating in the _terminate_pool() function, there is a call to result_handler.terminate() that occurs before terminating each worker in the pool. This causes the ResultHandler thread to exit the while loop in the finish_at_shutdown() function, because self._state will be set to TERMINATE. This means that on_state_change() does not get called for any tasks that have added results to the queue during shutdown.

I found this bug while implementing a fix for celery/celery#5998 and a fix for this issue is required in order to allow Celery tasks to complete gracefully during Celery shutdown. I have verified a fix in billiard locally and I will open a pull request.