Some homeowners in financial trouble in Michigan and nationwide say that their home is "paid off," but then add that they have "home equity loans." They might then say that those loans are overdue. Putting aside the terminology, those home equity loans are mortgages secured by their residences, and their homes are not "paid off," even if the original mortgage has been paid. The company holding the home equity loan can indeed foreclose on the home if not paid, just as the original mortgage holders could. One possible way to attempt to save the home is a personal bankruptcy.
A Chapter 13 bankruptcy, for example, ends all foreclosures or collection actions. To retain the home, you must start paying the current loan payments. The overdue past amounts can be paid off in installments over time, for up to 60 months.