For me, how I would react would depend on the kid, situation, and illness.
I know that Daughter usually gets very mouthy and beligerent when she is experiencing more anxiety than usual. I cut slack where I think appropriate, but for most part, disrespect, and insults, ain't tolerated in my house.
Generally, I take away what she values most. Computer, phone, or a piece of clothing she adores.
For me, using my sense of humor is a huge sanity saver. I try to use it at every opportunity.
About a year ago when we were in therapy session, she got very nasty and told me I was fat and ugly, and she was embarrassed to be seen with me. "Okay, fine, you do not have to be seen with me anymore". As fate would have it, I needed to go to the mall to get something after the session. Mall=Daughter's favorite place in the world. I figured why not start with the "Can't be seen with Mom" here?
I ordered Daughter to sit in the car (doors locked, of course) while Son and I shopped. Oh, she pitched a huge fit. "But, Darling, I'm only granting you your request not to be seen with your fat ugly mother". She threatens me with going inside the mall anyway. "Okay, fine", I say, "It won't be much fun without "the wallet" accompaning you. Plus, if you are not here when I get back to the car, I leave, and go home, without you (20 miles from home and I meant it)". I do not believe in empty threats.
When I got back about 90 minutes later, she, and an apology, were waiting for me.
For me it as much about respect as it is about being able to function in the world. A boss, or supervisor, isn't going to be so understanding about stress being the reason why you just insulted him, or her.