If the request's been sent, closing the browser won't be able to get it back. So it'll arrive at the server and do what it usually does, which might be deleting a file.
This makes sense, because how would the message be stopped? It might be traveling through optic fiber cables, and nothing is faster than the speed of light, so there's no way to catch up with it before it reaches the server.
Of course if there was any delay, the message may not be (totally) sent yet when you close the browser, in which case I guess it depends on the browser but it probably won't complete.