[3.10] bpo-45097: Add more tests for shutdown_asyncgens() (GH-28154) (GH-28159)

* bpo-45097: Add more tests for shutdown_asyncgens() (GH-28154)
(cherry picked from commit c2970fdec52788b6d9ff419ab7e31f255d87433d)

Co-authored-by: Serhiy Storchaka <storchaka@gmail.com>
diff --git a/Lib/test/test_asyncgen.py b/Lib/test/test_asyncgen.py
index 77c15c0..0814451 100644
--- a/Lib/test/test_asyncgen.py
+++ b/Lib/test/test_asyncgen.py
@@ -3,6 +3,7 @@
 import unittest
 
 from test.support.import_helper import import_module
+from test.support import gc_collect
 asyncio = import_module("asyncio")
 
 
@@ -1287,6 +1288,85 @@ 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):