About visa and residence permit

Hello, dear!
I'm a bit confused that's why I need your help. I'm Russian working in China in one of the schools. I've got my Z in Russia. When I came to China my company applied for the residence permit and now I got it under the company I'm working with. Soon I'll have to change the province and the company. Now I have some questions - what should I do with my residence permit and the Z? will my company cancel it?