Leases ending a specific date, but has "notice to vacate 60 days" need to give notice or not?

This is in CA. I have subletted a room - the lease ended May 31. The person said they were going to stay (verbally commited) and paid their May rent as usual. On May 29th they said they changed their mind. I have their last month rent deposit (since they hadn't used it) and they said they are entitled to it. Are they?