diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 987c011..8a69988 100755
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -1642,7 +1642,7 @@
             if not extfileobj and fileobj is not None:
                 fileobj.close()
             raise
-        t._extfileobj = extfileobj
+        t._extfileobj = False
         return t
 
     @classmethod
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 6986fc0..ceaa3aa 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -855,6 +855,12 @@
         tar.addfile(tarfile.TarInfo("foo"))
         tar.close()
         self.assertFalse(fobj.closed, "external fileobjs must never closed")
+        # Issue #20238: Incomplete gzip output with mode="w:gz"
+        data = fobj.getvalue()
+        del tar
+        support.gc_collect()
+        self.assertFalse(fobj.closed)
+        self.assertEqual(data, fobj.getvalue())
 
 
 class WriteTest(WriteTestBase, unittest.TestCase):