diff --git a/lms/djangoapps/grades/signals/handlers.py b/lms/djangoapps/grades/signals/handlers.py
index 8b64ddf2c3..4a5b4d5e26 100644
--- a/lms/djangoapps/grades/signals/handlers.py
+++ b/lms/djangoapps/grades/signals/handlers.py
@@ -57,6 +57,9 @@ def submissions_score_set_handler(sender, **kwargs):  # pylint: disable=unused-a
     user = user_by_anonymous_id(kwargs['anonymous_user_id'])
     if user is None:
         return
+    if points_possible == 0:
+        # This scenario is known to not succeed, see TNL-6559 for details.
+        return
 
     PROBLEM_WEIGHTED_SCORE_CHANGED.send(
         sender=None,
@@ -100,6 +103,7 @@ def submissions_score_reset_handler(sender, **kwargs):  # pylint: disable=unused
         course_id=course_id,
         usage_id=usage_id,
         modified=kwargs['created_at'],
+        score_deleted=True,
         score_db_table=ScoreDatabaseTableEnum.submissions,
     )
 
diff --git a/lms/djangoapps/grades/tests/test_signals.py b/lms/djangoapps/grades/tests/test_signals.py
index 0c2b65000b..896d18899c 100644
--- a/lms/djangoapps/grades/tests/test_signals.py
+++ b/lms/djangoapps/grades/tests/test_signals.py
@@ -130,9 +130,22 @@ class ScoreChangedSignalRelayTest(TestCase):
             'modified': FROZEN_NOW_TIMESTAMP,
             'score_db_table': 'submissions',
         }
+        if handler == submissions_score_reset_handler:
+            expected_set_kwargs['score_deleted'] = True
         self.signal_mock.assert_called_once_with(**expected_set_kwargs)
         self.get_user_mock.assert_called_once_with(kwargs['anonymous_user_id'])
 
+    def test_tnl_6599_zero_possible_bug(self):
+        """
+        Ensure that, if coming from the submissions API, signals indicating a
+        a possible score of 0 are swallowed for reasons outlined in TNL-6559.
+        """
+        local_kwargs = SUBMISSION_SET_KWARGS.copy()
+        local_kwargs['points_earned'] = 0
+        local_kwargs['points_possible'] = 0
+        submissions_score_set_handler(None, **local_kwargs)
+        self.signal_mock.assert_not_called()
+
     @ddt.data(
         [submissions_score_set_handler, SUBMISSION_SET_KWARGS],
         [submissions_score_reset_handler, SUBMISSION_RESET_KWARGS]