Your residence permit should normally remain intact but... considering that you left in bad terms or without a notice, if your ex-employer really want to screw you over by cancelling it they can, especially if they have good connections with the local government or the local PSB. If they have these connections it takes no more than a call to cancel it, if not they will have to do some paperwork but it can be done in a week or so. And NO they do not need your passport to do so, only your name, passport number and their business licence.

You will only know when you try to leave the country, if the immigration officers at the airport ask you to pay a fine (up to RMB5000 I think) for overstaying your visa.

If your former employer does not notify any Government agencies of your departure, your residence and work permit will remain valid (as long as he does not do it). But if by any chance your employer did notify that you are no longer employed there, then according to existing laws and regulations BOTH PERMITS will be cancelled, and your stay in China is ILLEGAL.
The proper way to resign an existing work opportunity is to while still employed, seek a new employer. Once you find one, and have their contract, then resign your current employer and go to PBS and Work Bureau within 10 days of resigning to notify the change of employer. If you do not do it within 10 days, if detained you will be given a few days to settle your affairs and deported, plus a heavy fine.
So, cross your fingers and good luck!

you cannot have two valid, different  visas at same time.  typically new employee enters china on z working visa, (good for 30 day), it is then canceled once residence permit is issued