diff --git a/Doc/ACKS.txt b/Doc/ACKS.txt
index 68aff56..a063827 100644
--- a/Doc/ACKS.txt
+++ b/Doc/ACKS.txt
@@ -238,3 +238,4 @@
    * Moshe Zadka
    * Milan Zamazal
    * Cheng Zhang
+   * Chris McDonough
diff --git a/Lib/multiprocessing/util.py b/Lib/multiprocessing/util.py
index 8a6aede..bc2d656 100644
--- a/Lib/multiprocessing/util.py
+++ b/Lib/multiprocessing/util.py
@@ -235,6 +235,12 @@
     Finalizers with highest priority are called first; finalizers with
     the same priority will be called in reverse order of creation.
     '''
+    if _finalizer_registry is None:
+        # This function may be called after this module's globals are
+        # destroyed.  See the _exit_function function in this module for more
+        # notes.
+        return
+    
     if minpriority is None:
         f = lambda p : p[0][0] is not None
     else:
@@ -266,7 +272,13 @@
 
 _exiting = False
 
-def _exit_function():
+def _exit_function(info=info, debug=debug, _run_finalizers=_run_finalizers,
+                   active_children=active_children,
+                   current_process=current_process):
+    # We hold on to references to functions in the arglist due to the
+    # situation described below, where this function is called after this
+    # module's globals are destroyed.
+
     global _exiting
 
     if not _exiting:
@@ -276,14 +288,25 @@
         debug('running all "atexit" finalizers with priority >= 0')
         _run_finalizers(0)
 
-        for p in active_children():
-            if p._daemonic:
-                info('calling terminate() for daemon %s', p.name)
-                p._popen.terminate()
+        if current_process() is not None:
+            # We check if the current process is None here because if
+            # it's None, any call to ``active_children()`` will throw an
+            # AttributeError (active_children winds up trying to get
+            # attributes from util._current_process).  This happens in a
+            # variety of shutdown circumstances that are not well-understood
+            # because module-scope variables are not apparently supposed to
+            # be destroyed until after this function is called.  However,
+            # they are indeed destroyed before this function is called.  See
+            # issues #9775 and #15881.  Also related: #4106, #9205, and #9207.
 
-        for p in active_children():
-            info('calling join() for process %s', p.name)
-            p.join()
+            for p in active_children():
+                if p._daemonic:
+                    info('calling terminate() for daemon %s', p.name)
+                    p._popen.terminate()
+
+            for p in active_children():
+                info('calling join() for process %s', p.name)
+                p.join()
 
         debug('running the remaining "atexit" finalizers')
         _run_finalizers()