Temporary Resident Permit

Hello,
I currently live in China working for a training center. I recently quit, and have gotten a new job with another school. The first employer is demanding that we give our passports back to the police so that they can cancel our Temporary Resident Permit, and put us on a 30 day short term stay. I have been told that this cannot be changed back into a Z type, and I would have to start the entire process over again.

My new employer has said that we do not have to do that, we just need our Foreign Expert Certificate and a release, but we do not have to let them cancel our Temporary Resident Permit.

Can you please let me know what my rights are here? Thank you