When you leave, ask the employer for a certificate of separation that states the contract term, the leaving date, the post and the years of work

In plain words

Whether you were dismissed, your contract ended or you resigned, the employer must give you a separation certificate (离职证明) when you leave, and transfer your personnel file and social insurance within 15 days. The certificate should state the contract term, the leaving date, the post and how many years you worked there. You need it to register as unemployed. If the employer won't give it, the labor department will order it to correct that, and if you suffer a loss because of it, the employer must pay you for it.