Well, desktop applications aren't entirely standard Java.  They follow a
different standard that's still in development.  You might try
generating a Java application rather than a desktop application.  This
will at least give you regular old Swing classes.

Desktop applications (the one you have) wrap Swing components for extra
functionality.  Assuming you have a JFrame you can access somewhere (I
don't recall how the desktop app handles Frames, off the top of my head)
you can use a window listener to receive window closing and window
closed events:

<http://java.sun.com/docs/books/tutorial/uiswing/events/windowlistener.html>

If you're talking about some other property, you'll have to be more
specific (at least for me).

Here is the home page for the Swing Desktop Application Framework.  Note
that they have not yet reached the early draft phase, according to their
own page.  I think you'd be better off to use plain old Swing for now.

<https://appframework.dev.java.net/>