diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index 8a123fa..a66726e 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -3683,7 +3683,7 @@
 
 class CTextIOWrapperTest(TextIOWrapperTest):
     io = io
-    shutdown_error = "RuntimeError: could not find io module state"
+    shutdown_error = "LookupError: unknown encoding: ascii"
 
     def test_initialization(self):
         r = self.BytesIO(b"\xc3\xa9\n\n")
diff --git a/Lib/test/test_struct.py b/Lib/test/test_struct.py
index 157efa1..4829fbe 100644
--- a/Lib/test/test_struct.py
+++ b/Lib/test/test_struct.py
@@ -7,6 +7,7 @@
 import sys
 
 from test import support
+from test.support.script_helper import assert_python_ok
 
 ISBIGENDIAN = sys.byteorder == "big"
 
@@ -652,6 +653,23 @@
         s2 = struct.Struct(s.format.encode())
         self.assertEqual(s2.format, s.format)
 
+    def test_struct_cleans_up_at_runtime_shutdown(self):
+        code = """if 1:
+            import struct
+
+            class C:
+                def __init__(self):
+                    self.pack = struct.pack
+                def __del__(self):
+                    self.pack('I', -42)
+
+            struct.x = C()
+            """
+        rc, stdout, stderr = assert_python_ok("-c", code)
+        self.assertEqual(rc, 0)
+        self.assertEqual(stdout.rstrip(), b"")
+        self.assertIn(b"Exception ignored in:", stderr)
+        self.assertIn(b"C.__del__", stderr)
 
 class UnpackIteratorTest(unittest.TestCase):
     """
diff --git a/Lib/test/test_sys.py b/Lib/test/test_sys.py
index 58701a1..c5bd8a4 100644
--- a/Lib/test/test_sys.py
+++ b/Lib/test/test_sys.py
@@ -855,6 +855,23 @@
         self.assertIn(b'sys.flags', out[0])
         self.assertIn(b'sys.float_info', out[1])
 
+    def test_sys_ignores_cleaning_up_user_data(self):
+        code = """if 1:
+            import struct, sys
+
+            class C:
+                def __init__(self):
+                    self.pack = struct.pack
+                def __del__(self):
+                    self.pack('I', -42)
+
+            sys.x = C()
+            """
+        rc, stdout, stderr = assert_python_ok('-c', code)
+        self.assertEqual(rc, 0)
+        self.assertEqual(stdout.rstrip(), b"")
+        self.assertEqual(stderr.rstrip(), b"")
+
     @unittest.skipUnless(hasattr(sys, 'getandroidapilevel'),
                          'need sys.getandroidapilevel()')
     def test_getandroidapilevel(self):