Companies in China do not have to do anything for you. Some will not even pay your salary, give you promised bonus or paid trips or vacations. You may ask for one, but do not haqve high hopes of getting it.

Companies in China don't have to provide a release letter.  You do need a release letter before you can get another job teaching.  This a thing they can hold over you.  The law says another school or training center needs that letter so they can file your paper work to get your Foreign Expert Certificate and Z visa.  The former employer canceles them so the new school has to apply for new ones.

Your company does not need to provide a thing. Especially after they release you they would probably want to get rid of you as fast as they possibly can and writing or having a release letter is something they are just not that interested in. I know you've been to centers that don't want to write anything all they want to do is have the discussion. It will be the same way when they release you I assume they will discuss it with you and then your free to go to get a better job or go to a better location.

Actually, under the Chinese Labor Law Code, they ARE required to provide a letter of release. They actually are. If they do it is another thing, but you need to insist rather strongly but politely.  Involve the local FEB if need and even the local PSB.  Letters of release are not just indigenuous to foreigners -- it's part of the Chinese system and Chinese corporate employees are also required to have one when leaving a job.

There are workarounds in place for obtaining a new work visa without one but they are so time-consuming and so stressful that the best advice I can give you, based upon 10 years of experience with this matter, is somehow, somehow to obtain the letter of release.  Additionally, you will need a letter of recommendation -- good, bad or indifferent.

It has become easier, however, in that most provinces now uniformly supply a combined letter of release / letter of recommendation form that you can easily obtain from your local or regional FEB.

Without this letter of release, your new employer would have to have a lot of pull at the local PSB or you might end up doing a Hong Kong run at your own expense.

Think it over carefully.

If you don't break the contract in anyway and in particular if you complete the time notice before leaving the company (like 1 month notice - see contract), then your next employer will have leverage to say you're legal and your old employer is illegal for withholding the release.

You should then get your release through the negotiations done by your new employer with the old one.

Re the above, actually no, it's more of a documents-based question than a question of the next employer having leverage, etc., etc.

When an application for a new residence permit is made at the PSB, they only consider whether or not there is a letter of release that accompanies the application.  If there are serious mitigating circumstances, the PSB may, must may intervene, directly or indirectly but more often than not, the visa process will be stayed and an "F" visa will be issued pending resolution of the matter.