diff --git a/pymongo/mongo_client.py b/pymongo/mongo_client.py
index d1794938f7..279eae5587 100644
--- a/pymongo/mongo_client.py
+++ b/pymongo/mongo_client.py
@@ -1596,8 +1596,14 @@ def _process_kill_cursors(self):
             try:
                 self._cleanup_cursor(True, cursor_id, address, sock_mgr,
                                      None, False)
-            except Exception:
-                helpers._handle_exception()
+            except Exception as exc:
+                if (isinstance(exc, InvalidOperation)
+                        and self._topology._closed):
+                    # Raise the exception when client is closed so that it
+                    # can be caught in _process_periodic_tasks
+                    raise
+                else:
+                    helpers._handle_exception()
 
         # Don't re-open topology if it's closed and there's no pending cursors.
         if address_to_cursor_ids:
@@ -1606,18 +1612,25 @@ def _process_kill_cursors(self):
                 try:
                     self._kill_cursors(
                         cursor_ids, address, topology, session=None)
-                except Exception:
-                    helpers._handle_exception()
+                except Exception as exc:
+                    if (isinstance(exc, InvalidOperation) and
+                            self._topology._closed):
+                        raise
+                    else:
+                        helpers._handle_exception()
 
     # This method is run periodically by a background thread.
     def _process_periodic_tasks(self):
         """Process any pending kill cursors requests and
         maintain connection pool parameters."""
-        self._process_kill_cursors()
         try:
+            self._process_kill_cursors()
             self._topology.update_pool(self.__all_credentials)
-        except Exception:
-            helpers._handle_exception()
+        except Exception as exc:
+            if isinstance(exc, InvalidOperation) and self._topology._closed:
+                return
+            else:
+                helpers._handle_exception()
 
     def __start_session(self, implicit, **kwargs):
         # Raises ConfigurationError if sessions are not supported.
diff --git a/test/test_client.py b/test/test_client.py
index 4d8b26400a..aee95692c6 100644
--- a/test/test_client.py
+++ b/test/test_client.py
@@ -1591,6 +1591,24 @@ def test_network_error_message(self):
             with self.assertRaisesRegex(AutoReconnect, expected):
                 client.pymongo_test.test.find_one({})
 
+    @unittest.skipIf('PyPy' in sys.version, 'PYTHON-2938 could fail on PyPy')
+    def test_process_periodic_tasks(self):
+        client = rs_or_single_client()
+        coll = client.db.collection
+        coll.insert_many([{} for _ in range(5)])
+        cursor = coll.find(batch_size=2)
+        cursor.next()
+        c_id = cursor.cursor_id
+        self.assertIsNotNone(c_id)
+        client.close()
+        # Add cursor to kill cursors queue
+        del cursor
+        wait_until(lambda: client._MongoClient__kill_cursors_queue,
+                   "waited for cursor to be added to queue")
+        client._process_periodic_tasks()  # This must not raise or print any exceptions
+        with self.assertRaises(InvalidOperation):
+            coll.insert_many([{} for _ in range(5)])
+
     @unittest.skipUnless(
         _HAVE_DNSPYTHON, "DNS-related tests need dnspython to be installed")
     def test_service_name_from_kwargs(self):
@@ -1613,6 +1631,7 @@ def test_service_name_from_kwargs(self):
                          'customname')
 
 
+
 class TestExhaustCursor(IntegrationTest):
     """Test that clients properly handle errors from exhaust cursors."""