bpo-45097: Add more tests for shutdown_asyncgens() (GH-28154)

diff --git a/Lib/test/test_asyncgen.py b/Lib/test/test_asyncgen.py
index a557cb5..bc0ae8f 100644
--- a/Lib/test/test_asyncgen.py
+++ b/Lib/test/test_asyncgen.py
@@ -1289,6 +1289,85 @@ async def wait():
 
         self.assertEqual(finalized, 2)
 
+    def test_async_gen_asyncio_shutdown_02(self):
+        messages = []
+
+        def exception_handler(loop, context):
+            messages.append(context)
+
+        async def async_iterate():
+            yield 1
+            yield 2
+
+        it = async_iterate()
+        async def main():
+            loop = asyncio.get_running_loop()
+            loop.set_exception_handler(exception_handler)
+
+            async for i in it:
+                break
+
+        asyncio.run(main())
+
+        self.assertEqual(messages, [])
+
+    def test_async_gen_asyncio_shutdown_exception_01(self):
+        messages = []
+
+        def exception_handler(loop, context):
+            messages.append(context)
+
+        async def async_iterate():
+            try:
+                yield 1
+                yield 2
+            finally:
+                1/0
+
+        it = async_iterate()
+        async def main():
+            loop = asyncio.get_running_loop()
+            loop.set_exception_handler(exception_handler)
+
+            async for i in it:
+                break
+
+        asyncio.run(main())
+
+        message, = messages
+        self.assertEqual(message['asyncgen'], it)
+        self.assertIsInstance(message['exception'], ZeroDivisionError)
+        self.assertIn('an error occurred during closing of asynchronous generator',
+                      message['message'])
+
+    def test_async_gen_asyncio_shutdown_exception_02(self):
+        messages = []
+
+        def exception_handler(loop, context):
+            messages.append(context)
+
+        async def async_iterate():
+            try:
+                yield 1
+                yield 2
+            finally:
+                1/0
+
+        async def main():
+            loop = asyncio.get_running_loop()
+            loop.set_exception_handler(exception_handler)
+
+            async for i in async_iterate():
+                break
+            gc_collect()
+
+        asyncio.run(main())
+
+        message, = messages
+        self.assertIsInstance(message['exception'], ZeroDivisionError)
+        self.assertIn('unhandled exception during asyncio.run() shutdown',
+                      message['message'])
+
     def test_async_gen_expression_01(self):
         async def arange(n):
             for i in range(n):