What will happen with ajax request? It will be always completed on server side but the response wont come anywhere? Or maybe ajax request on server side will be immidiately "killed?
I ask because I have some script which takes some time to run but user doesn't have to now the result - it's just fire and forget - maybe there is even some option in ajax to force it not to send any response?
The browser should kill the AJAX request, closing the connection to the server; however, this does not mean that your processing on the server is necessarily killed too: ignore_user_abort()
The server will complete the request, unaware that the client has "moved on." The server will return the response to the client like it normally does. The client will simply ignore the response.
So expect everything server-side to happen as normal, so the "fire and forget" method will work (since the client has moved on and has "forgotten"). But if you want to do anything client-side in response (which would negate the "forget" part) then there's no way for the new page to intercept the response. The browser will ignore it.