The regulation estipulates that work to be done by foreigners can only be offered to them after the company have proved to the Regulatory Board that there are no locals capable of doing this.  This is the reason why it is so common to see foreigners teaching English, and not as common in other fields.

If you are interested in more details, please visit
http://www.lehmanlaw.com/resource-centre/laws-and-regulations/foreign-presence/regulations-on-the-management-of-employment-of-foreigners-in-china-1996.html
to review the complete regulation in English

What HappyExpat says is the legality of it and very true. No Expat can take a job from a citizen.

The jobs outside of teaching are usually for managers or Expats who have a specialitiy in a certain field and have worked for the same company in their home country for at least 5 years.

The company gets the right to employ foreigners when they pay the fees to open up their business. Once they open up their business it is their right to hire or fire anybody they wish. That's why working for other people is not such a good idea unless it was for the government. The law doesn't look into who the company hires anyways that's why many schools in China  hire phillipinos from the phillipines and nigerians from nigeria to teach English. It will be 50 kuai cheaper for them per hour on what the student pays as opposed to hiring someone from a native speaking country.