I guess the important question would be...
Why are you keeping track of the session in a database to begin with?
I mean, if you are using sessions, then you have your way of tracking the user... There really is no need to keep track of the session variables in a database too... (unless you are collecting the info for some purpose, in which case, why delete the record from the database?)
You can't delete the record from the DB if they just close their browser at all (technically).
You could add some javascript to run a popup upon the page closing, and script the popup page to do the deletion. That's about the only way you could do it without clicking a link...