I heard of someone being let go before his contract ended. It was in GEPIK, but I can't remember which area of Gyeonggi-do, so it probably doesn't apply in your case.
Anyways, the school gave the teacher a lot of notice. They said that they could keep him for four more months and then gave him the option of leaving early so that he could transfer into another job, since the beginning of March is the best job start time.
I'm betting that it depends on your location and school. My salary is paid by 3 parties: the city, the school, and Gyeonggi-do. My co-teachers told me that some salaries are divided up differently. I really don't know how it works, but it has something to do with location, I think. This being Korea, there are probably 100 other factors too....
I should find out if my school can keep me today. I'm In Guri/Namyangju.