Your employer will issue you with the necessary paperwork so that you can exit China legally.At the airport,said paperwork,your residents' permit and your foreign experts' certificate will be taken from you.Then get on the plane,and breathe a sigh of relief.
Or,if you're game for a fresh start with a new Chinese employer,get a job offer fast,and said employer will do the necessary,hopefully,to get a new residents' permit for you in your new city,or get your current one altered to show your new employment details in the city in which you've been teaching and extend or replace it as and when necessary.
I hope you've got the gist.
A word of warning:under no circumstances try to depart China without first agreeing with your employer to terminate your contact - if you do that,you'll get grief at the airport!