Aging Care explains that children are not legally responsible for a deceased parent's debt. Even if power of attorney is held by one of the children, the debt does not transfer. However, there are some factors that could financially impact children of the deceased.
Generally, it is the estate of the deceased that is responsible for settling debts, not the children, but there are other things to consider. A CNN Money report cites examples of how an outstanding debt may be subtracted from an estate before inheritances are paid. If funds are not available to pay for debts, property may be sold to pay them, which could affect an inheritance, as well.