Yeah, if you're officially not working, that makes things a lot easier...
Otherwise, it's official policy of the Saloon that we cannot endorse or recommend that anyone ever live and work in China without having the full legal documentation...which for nearly all of us means a valid Residence Permit and Work Permit/Foreign Expert Certificate.
Being here illegally is risky and a very bad idea. Anyone who tries to tell you otherwise is wrong- and, if it's coming from an employer, a lie calculated to enrich themselves at your risk.
If you're working for a Chinese company, drawing a Chinese salary, and living in housing that isn't provided by your company, you must have a Residence Permit and Work Permit/Foreign Expert Certificate. That's simply the way it is. Get legal or get gone.