All states -- and many counties and municipalities -- run programs that offer financial benefits for funerals, burials, and cremation to families with low incomes.
Unfortunately, there is no good central resource that tracks all of them -- and what is available varies widely, depending on where you live. If your mother was receiving some type of public assistance during her lifetime, the family should first contact that agency. Otherwise, the best way to find out about the specific benefits offered in a particular locale is to do an Internet search of the state plus the county plus the words "burial assistance."
To secure any of the benefits, a survivor will have to fill out a brief application that the state or county agency will provide, usually including a brief listing of available cash, property, and other resources.