If there is an Ajax link which causes a redirect (if there is an exception or redirect to login page), only the complete handler is called. No call to the success handler (which wouldn't make much sense), but also no call to the failure handler. But as I said, the complete handler is called.
I understand the documentation in the way, that in all cases either success or failure handler should be called and then the complete handler. But in this situation no success or failure handler is called.