diff --git a/billiard/pool.py b/billiard/pool.py
index da4cc4e..e4c12a8 100644
--- a/billiard/pool.py
+++ b/billiard/pool.py
@@ -1659,7 +1659,12 @@ def _terminate_pool(cls, taskqueue, inqueue, outqueue, pool,
         debug('helping task handler/workers to finish')
         cls._help_stuff_finish(*help_stuff_finish_args)
 
-        result_handler.terminate()
+        # Send the sentinel to the result handler but don't terminate the
+        # result handler thread. This allows the thread to continue
+        # processing results in ResultHandler.finish_at_shutdown() until
+        # the cache is drained, ensuring that all task results are properly
+        # stored. A call to ResultHandler.terminate() is not necessary here
+        # because the thread will exit naturally when the cache becomes empty.
         cls._set_result_sentinel(outqueue, pool)
 
         if timeout_handler is not None:
diff --git a/t/unit/test_pool.py b/t/unit/test_pool.py
index fba1546..77ff91c 100644
--- a/t/unit/test_pool.py
+++ b/t/unit/test_pool.py
@@ -15,6 +15,8 @@ def get_on_ready_count():
     worker = inspect.stack()[1].frame.f_locals['self']
     return worker.on_ready_counter.value
 
+def simple_task(x):
+    return x * 2
 
 class test_pool:
     def test_raises(self):
@@ -56,3 +58,53 @@ def test_on_ready_counter_is_synchronized(self):
             pool.close()
             pool.join()
             pool.terminate()
+
+    def test_graceful_shutdown_delivers_results(self):
+        """Test that queued results are delivered during pool shutdown.
+        
+        Specifically, this test verifies that when _terminate_pool() is called,
+        the ResultHandler.finish_at_shutdown() continues processing results
+        that workers have placed in the outqueue.
+        """
+
+        # Create pool with threads=False so that the result handler thread does
+        # not start and the task results are allowed to build up in the queue.
+        pool = billiard.pool.Pool(processes=2, threads=False)
+
+        # Submit tasks so that results are queued but not processed.
+        results = [pool.apply_async(simple_task, (i,)) for i in range(8)]
+
+        # Allow a small amount of time for tasks to complete.
+        time.sleep(0.5)
+
+        # Close and join the pool to ensure workers stop.
+        pool.close()
+        pool.join()
+
+        # Call the _terminate_pool() class method to trigger the finish_at_shutdown()
+        # function that will process results in the queue. Normally _terminate_pool()
+        # is called by a Finalize object when the Pool object is destroyed. We cannot
+        # call pool.terminate() here because it will call the Finalize object, which
+        # won't do anything until the Pool object is destroyed at the end of this test.
+        # We can simulate the shutdown behaviour by calling _terminate_pool() directly.
+        billiard.pool.Pool._terminate_pool(
+            pool._taskqueue,
+            pool._inqueue,
+            pool._outqueue,
+            pool._pool,
+            pool._worker_handler,
+            pool._task_handler,
+            pool._result_handler,
+            pool._cache,
+            pool._timeout_handler,
+            pool._help_stuff_finish_args()
+        )
+
+        # Cancel the Finalize object to prevent _terminate_pool() from being called
+        # a second time when the Pool object is destroyed.
+        pool._terminate.cancel()
+
+        # Verify that all results were delivered by finish_at_shutdown() and can be
+        # retrieved.
+        for i, result in enumerate(results):
+            assert result.get() == i * 2
\ No newline at end of file