diff --git a/Lib/test/test_sys.py b/Lib/test/test_sys.py
index 84927a393f17593..0478f20cd33b4d4 100644
--- a/Lib/test/test_sys.py
+++ b/Lib/test/test_sys.py
@@ -1292,6 +1292,21 @@ def test_asyncgen_hooks(self):
         self.assertIsNone(cur.firstiter)
         self.assertIsNone(cur.finalizer)
 
+    def test_changing_sys_stderr_and_removing_reference(self):
+        # If the default displayhook doesn't take a strong reference
+        # to sys.stderr the following code can crash. See bpo-43660
+        # for more details.
+        code = textwrap.dedent('''
+            import sys
+            class MyStderr:
+                def write(self, s):
+                    sys.stderr = None
+            sys.stderr = MyStderr()
+            1/0
+        ''')
+        rc, out, err = assert_python_failure('-c', code)
+        self.assertEqual(out, b"")
+        self.assertEqual(err, b"")
 
 def test_main():
     test.support.run_unittest(SysModuleTest, SizeofTest)
diff --git a/Misc/NEWS.d/next/Core and Builtins/2021-03-29-19-50-34.bpo-43660.scTgag.rst b/Misc/NEWS.d/next/Core and Builtins/2021-03-29-19-50-34.bpo-43660.scTgag.rst
new file mode 100644
index 000000000000000..98419501d9e7b8a
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2021-03-29-19-50-34.bpo-43660.scTgag.rst	
@@ -0,0 +1,3 @@
+Fix crash that happens when replacing ``sys.stderr`` with a callable that
+can remove the object while an exception is being printed. Patch by Pablo
+Galindo.
diff --git a/Python/pythonrun.c b/Python/pythonrun.c
index 4c974cef39c78bc..b7b77d1f9ee3feb 100644
--- a/Python/pythonrun.c
+++ b/Python/pythonrun.c
@@ -932,7 +932,9 @@ PyErr_Display(PyObject *exception, PyObject *value, PyObject *tb)
         seen = PySet_New(NULL);
         if (seen == NULL)
             PyErr_Clear();
+        Py_INCREF(f);
         print_exception_recursive(f, value, seen);
+        Py_DECREF(f);
         Py_XDECREF(seen);
     }
 }