I will just wait for the executor to terminate with a specified timeout that you think it is suitable for the tasks to complete.
try {
//do stuff here
exe.execute(thread);
} finally {
exe.shutdown();
}
boolean result = exe.awaitTermination(4, TimeUnit.HOURS);
if (!result)
{
LOGGER.error("It took more than 4 hour for the executor to stop, this shouldn't be the normal behaviour.");
}