My understanding is the same as xwarrior's. I know someone who I am pretty certain had this happen, but with a student visa (I could be mistaken because this was quite a few years ago, but this is how I remember it). The guy had a student visa, stopped going to classes, the school cancelled his visa by simply informing the PSB that the guy was no longer a student. It was, if I remember correctly, part of a larger crackdown by that school on people using student visas simply as a way to stay in the country and not for actually studying anything. He didn't know this, tried to leave the country, and was fined for being on an expired visa.
I think what's missing here also is that whatever your chances are of getting away with it, really you're not entitled to keep your residence permit sponsored by a particular employer if you're not actually working for that employer anymore. This isn't the school trying to pull anything shady or untrustworthy, they're trying to cover their asses because they can't have foreigners running around the country doing who knows what when they're still technically responsible. It wouldn't fly in any other country (if someone sponsors my visa to say, work or study in the States, I can't just take that visa and go do something else entirely) and it doesn't fly in China. If the school decides to give you an extra month on your residence permit to go traveling or to give you some time to find a new job, that's their call, but I think expecting to keep the residence permit for an extra 5 months after you've stopped working there is a bit unreasonable.