You cannot handle the close button event consistently across many browsers.
As a result, it may be best to set an expiry on cache data.
For e.g.when you logon, you could set the cache expire to 30.
Response.Cache.SetExpires(DateTime.UtcNow.AddMinutes(30));
Another approach could be to have a logout button and add the following code -
Response.Cache.SetExpires(DateTime.UtcNow.AddMinutes(-1));
Response.Cache.SetCacheability(HttpCacheability.NoCache);
Response.Cache.SetNoStore();