Can foreign students come to China to work and study?

Well ... China is not so strict. If you want to be an English teacher or something, you won't be considered as working without signing a formal contract.

Work-study program refers to earning some remuneration through some part-time jobs during the semester to support the living expenses for study. Generally, there are special work-study departments or websites in universities, and outside enterprises will contact them to recruit some part-time jobs. For example, distributing leaflets, tutoring, translating, holding activities and so on. You can contact and have a look.