There is no server-side event that is raised when a page is left/closed. Also the Session_End event (mentioned in other answers) is not called when a page is left, since the user might navigate to other pages of the same web application (and therefore the session will continue to exist).
I can think of 3 possible ways to solve (or work around) this issue:
1 - use ViewState to store data with page-scope. This is what ViewState is made for, and unless you have a lot of data, it should not be a problem. If you have a lot of data, remember, that it will be serialized/deserialized and sent to the client/back to the server for every request (which may result in large requests and therefore bad performance).
2 - instead of putting the data into the session, put it into the Cache (with a low sliding expiration timeout). On your page, you can access your data in the same way as from the session, i.e. data = Cache["data"], but you have to be prepared that the data was removed from the Cache (you have to re-load it again from DB for example), if the time between two requests was bigger than the expiration time.
3 - use the client-side (javascript) onUnload event, and trigger some action (e.g. a ajax callback) to remove the data from the session. But I think the onUnload event is not reliable (it will not be fired in any case, e.g. when the browser is terminated by a crash or with the task manager, or if javascript is disabled).