If you have a partner in a home that is not paying his or her share of the expenses and have no written agreement as to the partnership, you cannot assume sole ownership of the property if a co-owner is not paying his or her share for its upkeep and debt load.If you are paying that person's share, you have an equitable lien upon the property for what you have paid. I suggest that you and the husband's cousin enter into a written partnership agreement over the duplex prepared by a real estate attorney. In it, expenses need to be covered as well as reimbursement. As you can see, the partnership agreement should have been done and signed before the property was purchased. Good luck.