This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
This permission only allows code to stop a thread if it has previously been granted permission to access that thread.
However, you shouldn't be calling the stop() method on a Thread anyway. The method was deprecated years ago because it is inherently unsafe and can cause bugs which are horribly difficult to trace. Consequently you should never grant this permission.
Closing an AWT window doesn't call stop() on any thread as far as I'm aware.