If a ralative is allowed to live with your parent and pays no rent then there is always the chance that he or she could claim some right to the property. However, to have an adverse possession claim the use has to be hostile, under claim of right, exclusive to your parent and without permission for a period of five (5) years.I do not see such being the case in your question. I suggest that your parent consult with a landlord tenant attorney about your matter futher for assistance and guidance.