The practice of the library has no legal basis. It should be said that there is a service contract for borrowing books and periodicals between you and the library. Both parties shall perform their respective rights and obligations in accordance with the contract. Then bringing books into the library and losing books are both violations of the contract and need to bear the responsibility for breach of contract. So how big should the responsibility be? If the library is clear about 10 times, if it strictly follows the contract, it should bear the loss of 10 times. However, China's contract law stipulates that if the liquidated damages are too high, they can be adjusted. Generally speaking, according to the deposit terms, 20% of the book price can be used as liquidated damages. 10 times is too high, and the court will not support it.
Although this is called a fine, it is actually a question of accountability for breach of contract.