Possibly you landlord has insurance coverage to cover the damage in the rental that you have caused by your cat. You should ask him or her about it. However, even if there is insurance that covers the damage, the insurance company for the landlord can pay the claim and then bring an action against you for the costs incurred for the repairs under the law.Whether that happens remains to be seen. I always recommend to tenants to pick up a policy of renter's insurance to cover a situation like you are writing about.