I've been searching for any reasonable example of a situation, when synchronous AJAX makes sense. I've found this SO question, where the author mentions window.onbeforeunload and claims, that "the request would never stop" if the AJAX call was asynchronous.
Can anybody explain this? I mean - window.onbeforeunload is fired when the user wants to close the tab. What had to be going on to make the tab still alive, even though somebody clicked to close it? Can somebody give more specific example?
He didn't say the request will never stop; he said it will never complete. That is, your code has no hope of ever getting the response back, because the execution environment (the window) would disappear from existence before that happened.
The tab will close when window.onbeforeunload exits with a truthy value. Thus, as long as it is running, the page is waiting for the return value, and not closing. This allows a synchronous AJAX to be sent, and for the response to be received and processed. If the request is asynchronous, the code constructs XHR object, then exits, and the page (and your code) goes away.
I have never tested this, but the answerer apparently believes (and I don't think it unreasonable) that the page might not stick around long enough for an async XHR to even be sent, let alone to receive a response. Thus, if you want to be sure the server receives the information that the user closed the page, you want to have the request synchronous.