changing the job, can I stay without visa but just on my residence permit?

Annie, your employer can cancel your employment certificate. However, she/he can't cancel your resident permit. He/she can report your situation to local entry and exit management bureau. The officers may cancel your resident permit. It's just a possibility. Your Z type has transformed into the resident permit. There is no worry about it.

If you plan to continue to work in China, you'd better end your contract with your employer peacefully because you need him/her to give you the release letter. It is required for you to renew your employment certificate and resident permit.

Theoretically, you should change your resident to a L type immediately as your job finished. But it's ok to stay with your resident permit too.