diff --git a/lib/questionlib.php b/lib/questionlib.php
index e7de6c840c4..e3c0639bd54 100644
--- a/lib/questionlib.php
+++ b/lib/questionlib.php
@@ -332,16 +332,18 @@ function question_category_in_use($categoryid, $recursive = false) {
 /**
  * Deletes question and all associated data from the database
  *
- * It will not delete a question if it is used by an activity module
+ * It will not delete a question if it is used somewhere.
+ *
  * @param object $question  The question being deleted
  */
 function question_delete_question($questionid) {
     global $DB;
 
     $question = $DB->get_record_sql('
-            SELECT q.*, qc.contextid
+            SELECT q.*, ctx.id AS contextid
             FROM {question} q
-            JOIN {question_categories} qc ON qc.id = q.category
+            LEFT JOIN {question_categories} qc ON qc.id = q.category
+            LEFT JOIN {context} ctx ON ctx.id = qc.contextid
             WHERE q.id = ?', array($questionid));
     if (!$question) {
         // In some situations, for example if this was a child of a
@@ -355,6 +357,15 @@ function question_delete_question($questionid) {
         return;
     }
 
+    // This sometimes happens in old sites with bad data.
+    if (!$question->contextid) {
+        debugging('Deleting question ' . $question->id . ' which is no longer linked to a context. ' .
+                'Assuming system context to avoid errors, but this may mean that some data like files, ' .
+                'tags, are not cleaned up.');
+        $question->contextid = context_system::instance()->id;
+    }
+
+    // Delete previews of the question.
     $dm = new question_engine_data_mapper();
     $dm->delete_previews($questionid);
 
diff --git a/lib/tests/questionlib_test.php b/lib/tests/questionlib_test.php
index 6f295e889a9..cd04aceb11d 100644
--- a/lib/tests/questionlib_test.php
+++ b/lib/tests/questionlib_test.php
@@ -273,6 +273,55 @@ class core_questionlib_testcase extends advanced_testcase {
         $rc->destroy();
     }
 
+    /**
+     * Test that deleting a question from the question bank works in the normal case.
+     */
+    public function test_question_delete_question() {
+        global $DB;
+
+        // Setup.
+        $context = context_system::instance();
+        $qgen = $this->getDataGenerator()->get_plugin_generator('core_question');
+        $qcat = $qgen->create_question_category(array('contextid' => $context->id));
+        $q1 = $qgen->create_question('shortanswer', null, array('category' => $qcat->id));
+        $q2 = $qgen->create_question('shortanswer', null, array('category' => $qcat->id));
+
+        // Do.
+        question_delete_question($q1->id);
+
+        // Verify.
+        $this->assertFalse($DB->record_exists('question', ['id' => $q1->id]));
+        // Check that we did not delete too much.
+        $this->assertTrue($DB->record_exists('question', ['id' => $q2->id]));
+    }
+
+    /**
+     * Test that deleting a broken question from the question bank does not cause fatal errors.
+     */
+    public function test_question_delete_question_broken_data() {
+        global $DB;
+
+        // Setup.
+        $context = context_system::instance();
+        $qgen = $this->getDataGenerator()->get_plugin_generator('core_question');
+        $qcat = $qgen->create_question_category(array('contextid' => $context->id));
+        $q1 = $qgen->create_question('shortanswer', null, array('category' => $qcat->id));
+
+        // Now delete the category, to simulate what happens in old sites where
+        // referential integrity has failed.
+        $DB->delete_records('question_categories', ['id' => $qcat->id]);
+
+        // Do.
+        question_delete_question($q1->id);
+
+        // Verify.
+        $this->assertDebuggingCalled('Deleting question ' . $q1->id .
+                ' which is no longer linked to a context. Assuming system context ' .
+                'to avoid errors, but this may mean that some data like ' .
+                'files, tags, are not cleaned up.');
+        $this->assertFalse($DB->record_exists('question', ['id' => $q1->id]));
+    }
+
     /**
      * This function tests the question_category_delete_safe function.
      */