I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this happened.
A tenant does not have a legal right to change their mind about moving into a property one they agree to do so, because you relied upon that promise by not continuing to show the property to other people and holding it for her. This dispute about carpet cleaning is not a sufficient reason for her to change her mind and not move in, especially because she made it impossible for you to actually clean the carpets by locking you out of the room.
The rule is that when there's no written lease, the tenant must give 30 days written notice of intent to vacate. Without that notice, she's responsible for rent for 30 days or until you find a new tenant to move in, whichever is less. If you manage to find a new tenant to move in before the end of October, then you'd have to pro-rate the rent and give her a refund for the days you had someone else there. You are requires to make reasonable efforts to find someone else to move in.
Cal. Civ. Code, Section 1950.5 requires that you send her a written notice within 21 days of the day she leaves, explaining how much of her deposit is being withheld and why. You can actually charge her for the cost of getting a new key for the bedroom door if she doesn't leave you a key (or changing the locks back). That notice MUST be sent, even if she's not getting any money back. That's important, because when a landlord keeps a deposit in bad faith, the tenant can sue for three times the deposit plus attorney's fees. Not sending the notice is evidence of bad faith. You can try asking her to give you a forwarding address for the purposes of sending her a letter. If she refuses, then the letter is sent to the last known address. She'll hopefully have mail forwarded by then, but if she doesn't, keep the letter to prove you sent it. The judge can open the sealed letter in court if it gets that far.
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