diff --git a/Lib/concurrent/futures/process.py b/Lib/concurrent/futures/process.py
index 63f22cf..ce7d642 100644
--- a/Lib/concurrent/futures/process.py
+++ b/Lib/concurrent/futures/process.py
@@ -423,6 +423,10 @@
         #   - The executor that owns this worker has been shutdown.
         if shutting_down():
             try:
+                # Flag the executor as shutting down as early as possible if it
+                # is not gc-ed yet.
+                if executor is not None:
+                    executor._shutdown_thread = True
                 # Since no new work items can be added, it is safe to shutdown
                 # this thread if there are no pending work items.
                 if not pending_work_items:
@@ -595,6 +599,9 @@
                 raise BrokenProcessPool(self._broken)
             if self._shutdown_thread:
                 raise RuntimeError('cannot schedule new futures after shutdown')
+            if _global_shutdown:
+                raise RuntimeError('cannot schedule new futures after '
+                                   'interpreter shutdown')
 
             f = _base.Future()
             w = _WorkItem(f, fn, args, kwargs)
diff --git a/Lib/concurrent/futures/thread.py b/Lib/concurrent/futures/thread.py
index 6e22950..b65dee1 100644
--- a/Lib/concurrent/futures/thread.py
+++ b/Lib/concurrent/futures/thread.py
@@ -87,6 +87,10 @@
             #   - The executor that owns the worker has been collected OR
             #   - The executor that owns the worker has been shutdown.
             if _shutdown or executor is None or executor._shutdown:
+                # Flag the executor as shutting down as early as possible if it
+                # is not gc-ed yet.
+                if executor is not None:
+                    executor._shutdown = True
                 # Notice other workers
                 work_queue.put(None)
                 return
@@ -145,6 +149,9 @@
 
             if self._shutdown:
                 raise RuntimeError('cannot schedule new futures after shutdown')
+            if _shutdown:
+                raise RuntimeError('cannot schedule new futures after'
+                                   'interpreter shutdown')
 
             f = _base.Future()
             w = _WorkItem(f, fn, args, kwargs)