Legal Question in Administrative Law in Pennsylvania

This sounds like a probate issue not administrative law. Administrative law relates to rule-making by government agencies.

Who died? Who is to inherit the house?

Homes are inherited subject to any existing mortgages unless the will provides otherwise. If the will does provide otherwise, then there would have to be a means of satisfying the mortgage from other assets.

The problem here it sounds like that the estate is for your mother and that the sister owns the house. In that case, we are not talking about inheriting a house subject to an existing mortgage but a debt owed to the estate. In such case, the estate cannot be held open indefinitely to permit repayment. Rather, if this is the case, the sister would have to keep paying the monies owed to the estate and try to look around for a lender who will be willing to take a home equity loan and pay off the loan held by the mother's estate.

I suggest that your sister talk with a probate law attorney about this.