California is a community property state. That means community debt as well. You are far from safe.
if she rents it (for the same amount) she cannot collect from you any longer.
If she sues and obtains a judgement it remains on your credit report for 10 years.
If she sued you, your defense is; it was uninhabitable due to the lack of a proper heating system. You provided notice of the defect. Her response was [whatever happens after notice is given].

