Always follow one simple rule:NEVER SURRENDER YOUR PASSPORT OR RESIDENCE PERMIT TO A SCHOOL except to acquire or update your permits.
Don't fall for any "safekeeping" BS...this is done solely to render you helpless. It's not even legal...you are supposed to be able to produce your passport and Residence Permit when requested. You're technically required under Chinese law to carry your Residence Permit at all times (although almost no one actually does this). Without your passport and Residence Permit, you won't even be able to check into a hotel if you travel.
You'll have to surrender your passport to your school and/or the police (probably through someone at your school) in order to get your Residence Permit, Work Permit and Foreign Exchange Certificate (FEC), or to renew these documents and/or your visa. This is necessary and reasonable. But once these things are processed, don't fool around. Don't even teach a class until all of your personal documents are safely back in your kung fu grip, after a reasonable time to get your Residence Permit, etc..(2-4 weeks). Don't sign a contract with anyone who requires this, and firmly and flatly refuse any requests to let them keep your documents. If anyone holds these documents against your will, stop teaching, immediately contact your nearest Consulate for help, and get out of that school ASAP. Make a xerox copy of your documents- do this yourself- and give them to the school to keep. Nothing more.
It's also not a bad idea to keep photocopies of your passport info page and your Residence Permit in your wallet so you can present them if approached by the police, without carrying the real documents around all the time and risking losing them. The police will not necessarily like this, but they will most likely grudgingly accept it.
Again: schools only hold your documents so that they can force you to take whatever swindles and abuse they choose to dish out. Never, ever let yourself be put in that position. Schools who won't swindle and abuse you (if there indeed are any) won't ask to hold your documents, either.
Note that your Work Permit is not issued to you for you to keep, and the FEC isn't always given to you and isn't really that big a deal. Don't sweat not getting those.