diff --git a/changelog.d/10690.bugfix b/changelog.d/10690.bugfix
new file mode 100644
index 000000000..059eea746
--- /dev/null
+++ b/changelog.d/10690.bugfix
@@ -0,0 +1 @@
+Fix a long-standing bug that caused an `AssertionError` when purging history in certain rooms. Contributed by @Kokokokoka.
diff --git a/synapse/storage/databases/main/purge_events.py b/synapse/storage/databases/main/purge_events.py
index bccff5e5b..3eb30944b 100644
--- a/synapse/storage/databases/main/purge_events.py
+++ b/synapse/storage/databases/main/purge_events.py
@@ -102,15 +102,19 @@ class PurgeEventsStore(StateGroupWorkerStore, CacheInvalidationWorkerStore):
             (room_id,),
         )
         rows = txn.fetchall()
-        max_depth = max(row[1] for row in rows)
+        # if we already have no forwards extremities (for example because they were
+        # cleared out by the `delete_old_current_state_events` background database
+        # update), then we may as well carry on.
+        if rows:
+            max_depth = max(row[1] for row in rows)
 
-        if max_depth < token.topological:
-            # We need to ensure we don't delete all the events from the database
-            # otherwise we wouldn't be able to send any events (due to not
-            # having any backwards extremities)
-            raise SynapseError(
-                400, "topological_ordering is greater than forward extremeties"
-            )
+            if max_depth < token.topological:
+                # We need to ensure we don't delete all the events from the database
+                # otherwise we wouldn't be able to send any events (due to not
+                # having any backwards extremities)
+                raise SynapseError(
+                    400, "topological_ordering is greater than forward extremities"
+                )
 
         logger.info("[purge] looking for events to delete")