Q: How does mortgage insurance assist the survivors of a deceased policy holder when they live in one of the homes that are covered under the policy?
A: It's not clear what you mean by "mortgage insurance." There is "private mortgage insurance" (PMI), which is a policy required when a home is purchased with less than a 20 percent down payment (or refinanced leaving less than a 20 percent equity stake). This policy protects the mortgage lender in case a borrowers defaults, and the borrower is required to pay the premium due as a part of the conditions of the loan being granted.
There is "credit insurance" (aka "credit life insurance") which is sometimes sold as mortgage insurance; more typically, it is sold to a homeowner as a means to pay off the mortgage in the event of the death of the homeowner, and this is where the confusion of terms can come into play.
Sometimes, this is coupled with the mortgage payment as an add-on charge.
If there was a form of credit life insurance policy in force, you'll need to review it carefully to see under what circumstances a claim will be paid. If two borrowers are on the loan, for example, it is not clear if the policy would pay a claim, since at least one party is still alive. If it does apply, the survivor would generally find themselves living in the home, mortgage free.
While it would seem like a great idea at its face, most experts don't recommend taking credit life insurance, since it simply further protects the lender (by paying off the loan). Rather, a low-cost term life insurance policy could be taken for the amount of the mortgage (or more) and the beneficiaries could decide how best those funds could be used, paying off the mortgage or not as they see fit.