diff --git a/server/src/main/java/org/elasticsearch/index/engine/InternalEngine.java b/server/src/main/java/org/elasticsearch/index/engine/InternalEngine.java
index da0243be5ca..fd247a6996c 100644
--- a/server/src/main/java/org/elasticsearch/index/engine/InternalEngine.java
+++ b/server/src/main/java/org/elasticsearch/index/engine/InternalEngine.java
@@ -1412,7 +1412,7 @@ public class InternalEngine extends Engine {
             return new DeleteResult(
                 plan.versionOfDeletion, getPrimaryTerm(), delete.seqNo(), plan.currentlyDeleted == false);
         } catch (Exception ex) {
-            if (indexWriter.getTragicException() == null) {
+            if (ex instanceof AlreadyClosedException == false && indexWriter.getTragicException() == null) {
                 throw new AssertionError("delete operation should never fail at document level", ex);
             }
             throw ex;
@@ -1515,7 +1515,7 @@ public class InternalEngine extends Engine {
                         doc.add(softDeletesField);
                         indexWriter.addDocument(doc);
                     } catch (Exception ex) {
-                        if (indexWriter.getTragicException() == null) {
+                        if (ex instanceof AlreadyClosedException == false && indexWriter.getTragicException() == null) {
                             throw new AssertionError("noop operation should never fail at document level", ex);
                         }
                         throw ex;
diff --git a/server/src/test/java/org/elasticsearch/discovery/DiskDisruptionIT.java b/server/src/test/java/org/elasticsearch/discovery/DiskDisruptionIT.java
index 4ac9fb5d32e..dac48d89e78 100644
--- a/server/src/test/java/org/elasticsearch/discovery/DiskDisruptionIT.java
+++ b/server/src/test/java/org/elasticsearch/discovery/DiskDisruptionIT.java
@@ -98,7 +98,6 @@ public class DiskDisruptionIT extends AbstractDisruptionTestCase {
      * It simulates a full power outage by preventing translog checkpoint files to be written and restart the cluster. This means that
      * all un-fsynced data will be lost.
      */
-    @AwaitsFix( bugUrl = "https://github.com/elastic/elasticsearch/issues/43626")
     public void testGlobalCheckpointIsSafe() throws Exception {
         startCluster(rarely() ? 5 : 3);
 
diff --git a/server/src/test/java/org/elasticsearch/index/engine/InternalEngineTests.java b/server/src/test/java/org/elasticsearch/index/engine/InternalEngineTests.java
index 59bbee9f1bb..38ade1ec746 100644
--- a/server/src/test/java/org/elasticsearch/index/engine/InternalEngineTests.java
+++ b/server/src/test/java/org/elasticsearch/index/engine/InternalEngineTests.java
@@ -5595,6 +5595,37 @@ public class InternalEngineTests extends EngineTestCase {
         expectThrows(AlreadyClosedException.class, () -> engine.acquireSearcher("test"));
     }
 
+    public void testNoOpOnClosingEngine() throws Exception {
+        engine.close();
+        Settings settings = Settings.builder()
+            .put(defaultSettings.getSettings())
+            .put(IndexSettings.INDEX_SOFT_DELETES_SETTING.getKey(), true).build();
+        IndexSettings indexSettings = IndexSettingsModule.newIndexSettings(
+            IndexMetaData.builder(defaultSettings.getIndexMetaData()).settings(settings).build());
+        assertTrue(indexSettings.isSoftDeleteEnabled());
+        try (Store store = createStore();
+             InternalEngine engine = createEngine(config(indexSettings, store, createTempDir(), NoMergePolicy.INSTANCE, null))) {
+            engine.close();
+            expectThrows(AlreadyClosedException.class, () -> engine.noOp(
+                new Engine.NoOp(2, primaryTerm.get(), LOCAL_TRANSLOG_RECOVERY, System.nanoTime(), "reason")));
+        }
+    }
+
+    public void testSoftDeleteOnClosingEngine() throws Exception {
+        engine.close();
+        Settings settings = Settings.builder()
+            .put(defaultSettings.getSettings())
+            .put(IndexSettings.INDEX_SOFT_DELETES_SETTING.getKey(), true).build();
+        IndexSettings indexSettings = IndexSettingsModule.newIndexSettings(
+            IndexMetaData.builder(defaultSettings.getIndexMetaData()).settings(settings).build());
+        assertTrue(indexSettings.isSoftDeleteEnabled());
+        try (Store store = createStore();
+             InternalEngine engine = createEngine(config(indexSettings, store, createTempDir(), NoMergePolicy.INSTANCE, null))) {
+            engine.close();
+            expectThrows(AlreadyClosedException.class, () -> engine.delete(replicaDeleteForDoc("test", 42, 7, System.nanoTime())));
+        }
+    }
+
     public void testTrackMaxSeqNoOfUpdatesOrDeletesOnPrimary() throws Exception {
         engine.close();
         Set<String> liveDocIds = new HashSet<>();