Session_End event is fired by a worker process. This also means that Session_End event might not have all the permission that a normal page request has. So if you are trying to connect to the SQL server with Windows account, Session_End event might not have required permission, although you can connect to the SQL in Session_Start event.
Session_End will fire after a given amount of time where session has been inactive. The given time can be changed globally in the web.config file with the time out attribute or for individual session with the help of Session.Timeout property.
Session_End will also fire when someone calls the Session.Abondon method. Note that the Session_End event will not fire immediately. As said before the Session_End event is fired from worker process. Hence the session ID will also be same.