These are always great questions; I've moved this topic to the Teaching area.
Oh, Gawd...
Yes, it IS possible to change jobs mid-contract...and there are ZILLIONS of horror stories about trying to do so. There are already many here around the Saloon.
The policy here is to encourage people to complete their contracts if it's possible...with recognition that it's definitely not always possible. When a situation becomes abusive, it's time to get the hell out.
Going back to Square One sucks, but it isn't the end of the world. If you're truly being cheated or abused, GET OUT!
The Release Letter allows you to move to another job and transfer your residence and Work Permits to the new school rather seamlessly and painfully. Without it, you're back to Square One: leave the country, re-enter on a new visa, and in general start the whole process all over. The letter simply states that you've been released from your contract and are eligible for new employment. However, the Letter MUST bear the official chop ("red stamp") of your school, so it's not something you can forge for yourself.
Generally, if you're on reasonably friendly terms with your outgoing employer, you should be able to obtain the letter no problem. If the school is pissed off at you, though, there's very little chance you'll ever get it. So the key here is to try to make your parting amicable, if you can. Of course, this isn't always possible even if you finish out your contract, given the tendency of so many schools to try and dodge their end-of-contract obligations to you...
Always make the Release Letter a part of your parting negotiations with any school...
In these days of horrific visa/permit rules, having docs in hand really counts for something...
One tidbit of trivia that might be useful, and that the schools won't exactly fall over themselves letting you know- in fact, many try to outright lie about this:
A school can only cancel your Residence Permit or visa if they have it physically in their hands.You can't deny your docs to the police if they request them, but you do not ever have to surrender your documents to a school functionary. Your residence permit will remain in effect until its expiration date- UNLESS you're silly enough to give it to them.