Yes you can work again after being fired/resigning. You just don't use anyone from that job as a reference. I was fired from one job with extreme prejudice (and I had it coming too) and the next one was even higher paying. He needs to come up with a good reason why he left. If I was him I'd say I got burned out. Everyone knows that teachers get burnt out.
I suggest he tries educational companies, academic publishing companies - related jobs where you don't actually work with children. Maybe as an account manager or something like that.
Good luck - I know unemployment is hard as hell.