diff --git a/indexing-service/src/main/java/org/apache/druid/indexing/seekablestream/supervisor/SeekableStreamSupervisor.java b/indexing-service/src/main/java/org/apache/druid/indexing/seekablestream/supervisor/SeekableStreamSupervisor.java
index ef65d6d22caa..0f2839e7fba6 100644
--- a/indexing-service/src/main/java/org/apache/druid/indexing/seekablestream/supervisor/SeekableStreamSupervisor.java
+++ b/indexing-service/src/main/java/org/apache/druid/indexing/seekablestream/supervisor/SeekableStreamSupervisor.java
@@ -1744,7 +1744,7 @@ public void runInternal()
       checkIfStreamInactiveAndTurnSupervisorIdle();
 
       // If supervisor is already stopping, don't contend for stateChangeLock since the block can be skipped
-      if (stateManager.getSupervisorState().getBasicState().equals(SupervisorStateManager.BasicState.STOPPING)) {
+      if (isStopping()) {
         logDebugReport();
         return;
       }
@@ -1752,7 +1752,7 @@ public void runInternal()
       synchronized (stateChangeLock) {
         // if supervisor is not suspended, ensure required tasks are running
         // if suspended, ensure tasks have been requested to gracefully stop
-        if (stateManager.getSupervisorState().getBasicState().equals(SupervisorStateManager.BasicState.STOPPING)) {
+        if (isStopping()) {
           // if we're already terminating, don't do anything here, the terminate already handles shutdown
           log.debug("Supervisor[%s] for datasource[%s] is already stopping.", supervisorId, dataSource);
         } else if (stateManager.isIdle()) {
@@ -2024,7 +2024,16 @@ private void killTask(final String id, String reasonFormat, Object... args)
   {
     Optional<TaskQueue> taskQueue = taskMaster.getTaskQueue();
     if (taskQueue.isPresent()) {
-      taskQueue.get().shutdown(id, reasonFormat, args);
+      if (isStopping()) {
+        log.debug(
+            "Not shutting down task[%s] because the supervisor[%s] has been stopped. Reason was[%s]",
+            id,
+            supervisorId,
+            StringUtils.format(reasonFormat, args)
+        );
+      } else {
+        taskQueue.get().shutdown(id, reasonFormat, args);
+      }
     } else {
       log.error("Failed to get task queue because I'm not the leader!");
     }
@@ -2034,7 +2043,16 @@ private void killTaskWithSuccess(final String id, String reasonFormat, Object...
   {
     Optional<TaskQueue> taskQueue = taskMaster.getTaskQueue();
     if (taskQueue.isPresent()) {
-      taskQueue.get().shutdownWithSuccess(id, reasonFormat, args);
+      if (isStopping()) {
+        log.debug(
+            "Not shutting down task[%s] because the supervisor[%s] has been stopped. Reason was[%s]",
+            id,
+            supervisorId,
+            StringUtils.format(reasonFormat, args)
+        );
+      } else {
+        taskQueue.get().shutdownWithSuccess(id, reasonFormat, args);
+      }
     } else {
       log.error("Failed to get task queue because I'm not the leader!");
     }
@@ -4562,6 +4580,14 @@ private boolean checkOffsetAvailability(
     }
   }
 
+  /**
+   * Whether this supervisor is in a {@link SupervisorStateManager.BasicState#STOPPING} state.
+   */
+  private boolean isStopping()
+  {
+    return stateManager.getSupervisorState().getBasicState().equals(SupervisorStateManager.BasicState.STOPPING);
+  }
+
   /**
    * Call {@link FutureUtils#coalesce} on the provided list, and wait for the result.
    */
diff --git a/server/src/main/java/org/apache/druid/indexing/overlord/supervisor/SupervisorStateManager.java b/server/src/main/java/org/apache/druid/indexing/overlord/supervisor/SupervisorStateManager.java
index f30517d1b225..f64f390fc566 100644
--- a/server/src/main/java/org/apache/druid/indexing/overlord/supervisor/SupervisorStateManager.java
+++ b/server/src/main/java/org/apache/druid/indexing/overlord/supervisor/SupervisorStateManager.java
@@ -127,7 +127,9 @@ public SupervisorStateManager(SupervisorStateManagerConfig supervisorStateManage
    */
   public synchronized void maybeSetState(State proposedState)
   {
-    if (BasicState.STOPPING.equals(this.supervisorState)) {
+    if (BasicState.STOPPING.equals(this.supervisorState) || BasicState.STOPPING.equals(proposedState)) {
+      // STOPPING takes precedence over all other states
+      supervisorState = BasicState.STOPPING;
       return;
     }