unfortunately this is not as easy to answer as it seems it should. It doesn't necessarily violate cohabitation. Are they living together in any way shape or form? Also, what is the purpose of the co-mortgage? Is this an investment property?
I suggest you see an Attorney to discuss the specifics of your case. If you wish I would be happy to give you a free consultation.
First, the terms of the final divorce order may dictate how the court can address this situation. If the order is silent, I agree with Atty Balter, the nature of the cohabitation is important. If she takes on a tenant, that probably would not change things unless it changes her financial situation. However, the nature of the cohabitation is something the court can consider as it has wide discretion when determining whether to modify the court order.
Note: This response DOES NOT constitute legal advice and therefore no specific action should be taken in reliance thereon. No attorney-client relationship is created through this response. You should speak to an licensed attorney in your state who is competent to answer your question before taking any action with regard to this question.
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