That's what they do.

The schools that use these agents, usually don't have a license to recruit foreign teachers. The police have visited such schools and warned foreigners that if they continue to teach there, they will face deportation.

I sometimes wonder if foreign teachers that are unlucky enough to work for such agency, should form an online database of these kind of schools. Unfortunately, their lack of Chinese may prevent them from giving accurate details, but maybe if one or two foreigners with good Chinese and the use of Baidu can help them out. People with the right contacts could grass these schools up to the right people in the PSB, when the teacher has safely left that company.

Hell, people even get financial rewards for grassing up the illegal teachers these days too. Might feel guilty about getting a new teacher in shit, but... It might work out better for them.