I have never had this happen to me, but I'm sure other people have. From my perspective, there is nothing really stopping them from leaving; you cannot force them to stay and keep their obligations as a moderator, but at the same time, you cannot force them into leaving and getting considered yourself as a result. Either situation would result in some form of guilt occurring in the long run, and that is never good. The best thing to really do is to tell them that they should think things through and do what they see as the best choice.
Though, if I had to go for one or the other, I would lean toward them staying, depending on the situation. If it's a minor matter with stress or something like that, then staying could help, as long as it comes with a bit of time away from the forum. If the issue is more dire (i.e. a personal loss, hospitalization, etc.), then I'd steer them in the direction of leaving. From my perspective, their suffering will not be helped as much online as it would in the real world.