What happens if someone dies without a will and creditors are owed?

My father is dying. My parents do not have much money (that is really an understatement) However, one thing my father does have is a family home in northern Michigan. My mother's name is not on the deed, it is only in my father's name. After my father passes, my mother plans to move there and live since they are losing their home in Metro Detroit. I am worried she will not end up with the house. There are creditors (about $20, 000 in debt in his name only, credit cards and medical bills) She dos not have the money to pay the creditors. Will the creditors get the house? I think the way this would work is, since the house is not in both of their names it will go to probate, the creditors will need to be paid before the "estate" can be finalized. Will the court sell the house to pay the creditors? Is there anything that can be done to save the house for her? Thank you.