I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
An oral agreement to let someone lease or sublease real estate is binding in California. It just means that you've created a month-to-month agreement that either of you can terminate at any time with 30 days notice.
Tenants and subtenants actually have the same rights - when you agreed to sub lease the room, you became a sub-landlord, subject to the requirements of the California Civil Code. See Section 1940. And what that unfortunately means is that, yes, the subtenant can sue you. This is true even if you didn't have consent from your management company to enter a sublease, because it's up to you to verify that before agreeing to a sublease. So, if there are problems with the room, or if the subtenant has to leave because your lease didn't allow them to be there, they can sue for damages. Since they are by default given only a month-to-month lease, the damages are usually limited to the cost of staying elsewhere for one month (minus what she was supposed to pay you).
Also note that, because the civil code applies, it would be illegal for you to change the locks or shut off utilities to get her to leave. She could actually sue you for a penalty of $100 for each day she was denied access to the property, plus her attorney's fees (which could equally total a few thousand dollars). Section 789.3
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