Run query on browser close

I build a chating system. Now When user logout from system and then after some time login again then he saw a some messages notifications. These notifications are about those messages which was received when he was logout. I run a update query on logout button. When user clicks on logout first an update query is run where i change its status from 1 to 0 and than I expire its session. Now my problem is this when user cant click on logout button and close the browser or He face some internet issues. On closing browser session is also expire. Now How I run update query In this case where he cant click on logout button but its session is expire.

Thanks.