It has never been legal to work for a third party. You have been working illegally. I used to run into foreigners in the PSB where I lived and Id be like hey where do you work, they would say oh I work in and theyd name some city far away. Id be like why are you coming down here to get your visa and not in your own municipality. They were just like I don't know my school told me to. What was actually going on was they worked for an illegal fake school as you do and the person in charge of their school knew someone in my city who had a legit school so they would pay them prolly 10 thousand to 15 thousand to use that schools license to get the foreigner a z visa and res perimt FEC etc.

Ask to see your schools license.
The US is shit, their website tells people to have a z visa to work legally. That is only half the story. I know so many foreigners in china who think they are legal, but they are not. You have to have the right visa and certificates, but it has to actually be sponsored by the place you work at. It is very hard to get those certifications.

I would suggest not resigning.