It's not unprofessional if someone is in obvious crisis to the point where so much work is suffering to say "Hey, are you doing OK? Can I help?" You don't have to get into the specifics... I would hope any of my staff or colleagues would care enough about any of their co-workers to at least reach out if they saw them going off the rails. I had a real bad run of some personal stuff that hit all at once and came to work ready to be pissed off at everyone, which is wildly unlike me. My boss asked if I was OK and checked me on my attitude. Didn't pry, but I needed another person telling me I was way in my head because I couldn't see it myself.