Q u o t e: If you close the browser without logging out you still stayed logged in for a while. You should always log out before you close your browser.
Well your session will continue to exist server-side but you can't make use of it anymore. Any new browser started goes thru the whole session id handshake thing again. Try it here. Login and jump into a thread then close your browser. Restart it right away and re-enter the forum. Your old session is gone and you have to login again.
Venture to the Realms Beyond to get off the beaten path.