Hi, Mark:
There is no ILLegal schools in China, but most of them might not be licensed. If not, it's not authorized to hire foreign teachers. Most of the elligals still ads for teachers but, by delaying the process. Once you taught a certain time for them, and they would fire you and get another for some other period of time.... Some even ask you if you wanted to have a contract or didn't matter, in a gesture that they could get a license for you, but actually they might not be able to.
Alex