If you just want to do something when the application is shutting down, you can hook the shutdown using this code:
    Runtime.getRuntime().addShutdownHook(new Thread(new Runnable() {
        public void run() {
            // Do what you want when the application is stopping
        }
    }));
However, this will not allow you to not close your window. If you need to check something before really exiting, you can override the windowClosing event:
addWindowListener(new WindowAdapter() {
    public void windowClosing(WindowEvent e) {
        // Do what you want when the window is closing.
    }
});
Note that the first solution - using the shutdown hook - has the advantage that it is not related to a window event, and will be executed even if the application is stopped by another event (except, of course, if the Java process is killed brutally).