The issue of the current bug is unguarded access to mi->slave_running 
by the shutdown thread calling end_slave() that is bug#29968 
(alas happened not to be cross-linked with the current bug)

Fixed:

with removing the unguarded read of the running status
and perform reading it in terminate_slave_thread()
at time run_lock is taken (mostly bug#29968 backporting, still with some
improvements over that patch - see the error reporting from 
terminate_slave_thread()).
Issue of bug#38716 is fixed here for 5.0 branch as well.

Note:

There has been a separate artifact identified - 
a race condition between init_slave() and  end_slave() - 
reported as  Bug#44467.

mysql-test/r/rpl_bug38694.result:
  a new results file is added.
mysql-test/t/rpl_bug38694-slave.opt:
  simulating delay at slave threads shutdown.
mysql-test/t/rpl_bug38694.test:
  A new test to check if a delay at the termination phase of slave threads
  could cause any issue.
sql/slave.cc:
  The unguarded read of the running status is removed. Its reading is done in
  terminate_slave_thread() at time run_lock is taken;
  Calling terminate_slave_threads(skip_lock := !need_slave_mutex) in the failing branch of start_slave_threads() which is bug#38716 issue.
sql/slave.h:
  removing terminate_slave_thread() out of the global interface scope.