Can closing the browser terminate the PHP script on the server?

Question

Say a user clicked a button, which resulted in a jquery ajax request being sent to my server.

The server begins a complicated process in response to the ajax request

Answer 1

Unless it's launched as a background process i.e. with the & at the end... it will just terminate.

Closing browser a bit more to it... It will stop eventually, but will process for a little while before web server realises connection is gone.