Can I stay in China to wait for my Z visa and residence permit to be renewed?

I am presently waiting for a new Canadian passport which should arrive no later than August 2. My original passport containing my Z type and Residence Permit stamps expires on August 11. Since I want to start a new TEFL job in Chongqing this September, I need the new passport. So I am wondering if I can apply for the pair of renewals and stay in China although the application process may be completed after August 11. Or do I have to apply earlier that would allow the application to be completed before then so I could stay in the country? Different provinces might have different rules, but my new employer has assured me that I can wait without having to leave the country. Your feedback, please!