I've had Napster stay resident in memory, even though I've closed down the application window.
My advice is to try this:
Start napster application, connect to the Napster Server, then close the Napster application.
Now do a <Ctrl><Alt><Del> and see what applications are still running - not saying that it will be. But it's worth investigating.
Ps. I only noticed it when, having shut down my Napster window, and several minutes later my disc drive whirred into life. On another occasion I had a message on my screen in the morning telling what a great music collection I had - I'd disconnect prior to going to bed (so I thought).