I work on processing visa applications for companies in China, and what KGB says here is absolutely correct. Current regulations in China absolutely require a RELEASE LETTER from the organization sponsoring your current visa if you wish to change to another company.

Whether your current or prospective employer(s) are public or private schools or universities is irrelevant.

Without a release letter the only other option is to return to your native country and apply for a new visa. To do this you will need a hard copy of an invitation letter from your new company. No longer is going to Hong Kong an option, it must be in your native country (where your passport is issued)

Employers in China are not required to provide specifics or details stating their reasons for withholding a release letter, and teachers have little or no recourse in the matter. Be on the good side of your FAO and school manager - the law is most definitely in place to protect schools.

Also be aware that a school is well within their rights to pull a visa from an employee for gross contract violation - and most would consider running away at midnight to be such a circumstance. Should this happen you could have extreme hassles and possibly hefty fines (Y500 per day) when trying to exit the country.