If I get you correctly, you want to know when a tab/window is effectively closed. Well, AFAIK the only way in JavaScript to detect that is to use either onunload or onbeforeunload events.
Unfortunately (or fortunately?), those events are also fired when you leave a site over a link or your browsers back button. So this is the best answer I can give, I don’t think you can natively detect a pure close in JavaScript. Correct me if I’m wrong here.