diff --git a/Lib/threading.py b/Lib/threading.py
--- a/Lib/threading.py
+++ b/Lib/threading.py
@@ -552,6 +552,10 @@
         self._tstate_lock = None
         self._started = Event()
         self._stopped = Event()
+        # _is_stopped should be the same as _stopped.is_set().  The bizarre
+        # duplication is to allow test_is_alive_after_fork to pass on old
+        # Linux kernels.  See issue 18808.
+        self._is_stopped = False
         self._initialized = True
         # sys.stderr is not stored in the class like
         # sys.exc_info since it can be changed between instances
@@ -707,6 +711,7 @@
 
     def _stop(self):
         self._stopped.set()
+        self._is_stopped = True
 
     def _delete(self):
         "Remove current thread from the dict of currently running threads."
@@ -793,7 +798,7 @@
         assert self._initialized, "Thread.__init__() not called"
         if not self._started.is_set():
             return False
-        if not self._stopped.is_set():
+        if not self._is_stopped:
             return True
         # The Python part of the thread is done, but the C part may still be
         # waiting to run.