From my own experience I found the company I work with to be very accomodating.
The problem is they wouldn't have known anything about it unless I said something. You don't have to say anything more than "I'm having some personal problems and am not fit to fly tomorrow", embarrasing details are not necessary.
I guess what the company did do, is make it clear that if you don't feel mentally fit to fly, then it is ok to say so. So when the time came that I had too much on my mind, I had the confidence that my problem would be received in the right way.
That is probably the best a company can do about problems like these that can be hidden so easily, try to provide an environment in which the employees feel comfortable grounding themselves when necessary.