If you have an X (student) visa and you stop going to school your school can terminate your visa and you will have to leave the country – normally you have 10 days to do so.

Employers cannot usually cancel your residence permit (what your visa is converted to when you get a job and apply for all the proper paperwork) without your passport, but they can cancel your work permit and refuse to give you a release letter. Without a release letter it’s pretty much impossible to legally find new work. If you want to leave your company but keep your Z visa, you need your employer to give you a release letter and you need to find a new company that can sponsor you. If you can’t do that you probably want to go to Hong Kong and apply for a different kind of visa.

Sorry, daniel159, but my experience tells you´re wrong.
When i cancelled my contract with my old company, they cancelled my visa. When i asked why they did that, i was informed it´s the law. They will cancel that visa, and issue a temporary one (mine was for one month).
I double checked with the local authorities, and they confirmed, even saying that´s not an usual practice.

100% they can cancel your visa but try to resolve the problem by mutual understanding.

Yes they can. But you can get another Visa.

A company is supposed to cancel your visa after the contract is terminated, even they want to do you a favor, they might not want to get troubles by themselves.

From what I have seen, it depends. My old school tried to do that to a girl who skipped after a month to work for a uni. They threatened her and it turned out they could do bugger all. She worked for the uni until her visa ran out then the uni got her a new one.

Yes. A school can cancel your visa, or have your residence permit revoked.

However, it really depends; don't forget that This Is China (TIC). Some schools will let you stop going to class if you ask for permission -- so as long as you continue to pay tuition and obey the laws. Make sure you do that before bailing on the school. They will still call you multiple times and ask if you're safe now and then, so be prepared to answer the phone.

The new (actually just being enforced strongly now) Laws are very simple.

1. You must only work for and be paid by the company or school that provided you with a Work Permit (non-professional position) or a Foreign Expert Certificate (Professional positions that includes teaching of any type).

2. You must work under the correct Permit and that Permit must be obtained in your Company's/School's name, not another entity or you're illegal.

3. If you leave employment, your employer must cancel your Work Permit/Foreign Expert Certificate and your Residence Visa, providing you with a 30 day, 0 Entry, non-extendable Tourist Visa UNLESS a new company/school has made arrangements with your employer to change it over.

4. In the event you decide to simply "disappear," the company or school is now obliged to go to the Employment Bureau or Foreign Expert Administration Bureau and cancel your Permit and then to the Public Security Bureau to cancel your visa.

5. If the Employer cancels your Permit and Visa, you will find out when you go to the PSB or when you try to leave the country. You will be fined up to RMB 200,000 for living/working illegally and fined RMB 500 per day for every day from the time your visa was canceled. It is of note to add that you will be a guest of the government until all fines are paid in full, that your air ticket out is paid for and they will escort you to the airport and onto the plane.

China has improved, strengthened and enforced their Immigration and foreign employment laws (and penalties) to match western countries.

6. Contrary to popular belief, you will have a criminal record registered with Interpol if you're caught breaking Employment and/or Immigration laws. Don't forget that China is one of the 6 vetoing nations in the UN and that Interpol is the data collection agency for all member countries to check when you want to enter their countries.