My mother's in debt :(?

Well, the brief story is that my mother collected a mound of debt over her lifetime ($1,000's) to the point that I’m am dead sure she wont be able to pay it off when her time is up (death). My question is, with all the debts she didn't pay off and still owes will that debt carry over to her closest relatives? i.e. me her son left to pay the remaining fees.