you break the contract they'll cancel the visa.

It depends on why you breaking the contract and if you plan on working at another company or school? You did not mention what type of work you are doing, so I will assume teaching. Technically to change teaching jobs you need a letter of release from your previous employer, this letter should be stamped by the school and the local PSB.Without this letter the new school cannot get a foreign experts certificate issued.

If you just leave the school, it is up to the school to cancel your visa, some do some do not. This might cause you trouble when you try to exit the country or get a new visa issued.

There's a government for each province in China; if you break a Z Visa the government of the province you work in will take note and may refuse you another work related VISA in the next years (but you can still try, nothing's sure). But Visa for studies should be fine (X Visa).
In terms of work, the school you worked for will take revenge, not letting you use your Foreign Expert Certificate for another Z Visa job, so you might not be able to get another Z Visa in the near future anywhere in China, although eventually things will sort out one way or another; like you can get a job on a Business VISA or let your new employer put pressure on your old school for them to eventually release your Foreign Exp Cert to them.
I even heard that a whole new Foreign Expert Certificate can be made, but that depends on the local government and how good the schools’ relations with that local gov are.
Take note that there are 2 kinds of Certs in China: Foreign Exp Certificate for all education related jobs, and Scientific Expert Cert (not sure the exact name) for other jobs.
Worth knowing that you’ll probably never see your cert; it’s the property of your employer, who passes it on to your next employer.
The Foreign Exp Cert has an expiry date on it, but even after expiration you still need a release from the last employer who has it to get your next Z Visa job.
In the end, it’s just loads of red tape (bureaucracy); and where employers and governments like you and get along well together things become very easy.
However when you break a contract you burn bridges, make relationships bad, and that’s what you don’t want in China.
If you break a Z Visa contract, change province, and eventually start working on a Business VISA that doesn’t tie you down, cos F Visas (business) can be broken without future consequences I think.
However, regarding the Chinese gov and it's VISA Bureau the F Visa is not proven work experience, because F Visa is not official employment; only Z Visa is.