Except for putting a timeout on your sessions - not really. The only way that comes to mind is the onbeforeunload
JavaScript event that fires when the user leaves the current page, but that event doesn't know where the user is going. You could however, if you really want to do this, maybe build something based on the following hacky workaround (untested):
set an onbeforeunload
event that sends an AJAX call to your server. (How to do this successfully - so the call gets through before the page gets closed - is an issue of its own, a search for "onbeforeunload ajax" on SO should yield some results.
The Ajax call would start a countdown saying that this user's session is about to die in, say, fifteen seconds.
If the user is leaving your site, the countdown applies.
If the user is going to a different page on your site, you clear any "die" countdowns when serving the next page.
This is likely to be shaky because it could happen that an Ajax request starting a countdown arrives at the server after the next page has already eliminated that countdown. But if you really need to do this, this may be a direction. Works for users with JS enabled only, of course.