My mother rented her home to two men, and left utilities with a large balance. They never paid the balance, therefore my mother was responsible for paying the remaining balance for the utilities in order to re-install them, since she was going to put the house on the market. Later one of the persons 'abandoned' their belongings, and my mom kept them in her house for over a month and a half. Later they remodeled the home and the stuff were left outside and the wind and rain came and destroyed all his belongings. This happened in February and the person never claimed their belongings, now it's October and the person is asking for them. Otherwise they will sue her... What should she do?

How much do you think the stuff was worth? Did someone take pictures and do an inventory of the items?

Bailment varies state to state. Did your mom's lease have language about the property of the renter upon leaving, read carefully. Did mom try to contact the lessee about the utilities, the rent or the property?

Did your mom sue them for the utilities, unpaid rents, cost of repair and moving out trash

So you merely deny them, and let them sue, ( you don't have a choice since you don't have it to give them)