I need your advice about my visa

Hello everybody! I'm teaching at school. Soon my contract will be completed and I plan to go to a different province to take my chances here. I have a residence permit (which means I have a z type one?not sure here, and, of course, chinese staff at school can't explain to me). What they suggest is when I finish here I will go to a different province under the same residence permit(because it takes so much effort for them to cancel it and to give me another type ) So they let me use this one while I'm travelling. But if I find a job in a new province I'll just contact them and they will provide me with all the necessary documents(like reference letter, release letter and all that i will need for a new residence permit). But I need your advice. Is it really worth doing? Will it be easy for me then to get the documents and to change mine? Can they do it without my presence?