The amount of money he spoke of is for breach of contract. When the school returns your FEC (assuming you were working legally) they are confirming that the contract was honored.

I've never heard of a university paying for the summer AFTER the contract is finished and when a new one is not signed. All payments and consideration must be completed prior to contract completion.

If you've completed the contract, you should have a letter of reference and/or release from the FAO and/or department. If those documents are in your custody, you are able to confirm to your new employer that you completed your contract with your prior employer; your new employer will require that document.

Of course, if you were working illegally or at a corporate school, all bets are off. But in that event, the 'school' dare not contact the PSB about an illegal employee of theirs.

Also, only the university FAO department is usually aware of all these regulations, a university Chinese teacher is usually clueless on these matters. His belief about his ability to bully you are either a result of his ignorance or his expectation of yours.