Q: Is it legal for the executor of an estate to force a benificiary to pay for a mortgage on a house they inherited?

A: "inheritance" doesn't mean the bank loan is forgiven. It must be either paid off from Estate funds, or refinanced by the person inheriting the property. A "quitclaim" deed (one without the usual warranties of title) means the mortgage lien/loan obligations of the dead person remain. This is likely a violation of the loan and mortgage documents, anyway.

Where the Estate or heirs cannot afford to refinance or payoff the lien, then the property must be sold.

A: It might be easier for you to think of this a different way. If the course was inherited by both sister, each has the right to use the undivided whole, and either has the right to demand that it be sold and the proceeds after paying off the mortgage split. If you cannot reach another agreement, that's what needs to happen. If there is a mortgage, that value should be deducted from the value of the house when computing the payoff. If the paid off sister is liable for the mortgage and cannot get taken off by the lender, then you need to refinance or pay off the mortgage.

A: When a house has a mortgage on it, the mortgage will need to be paid one way or another. Either the estate will pay off the loan with other cash and deed the house free and clear, the house will be sold and the loan paid at closing or the house will be conveyed to heirs "subject to" the mortgage or one heir will buyout the others with a refinance to cover both the buyout and paying off the existing loan.

It is not clear from your post what you mean by "inherited" - what can/should happen next depends on where things are in the process. Has the estate closed and the property already been deeded to the siblings? Or is the property still in the estate and the Personal Representative is asking whether the other heir is willing to take the property subject to the legal obligation to pay the loan?

If the property is already deeded out of the estate, the law presumes that co-owners will jointly contribute to property expenses. If one or the other does not contribute their "fair share" then the law allows a forced sale. Usually that is the worst of all possible outcomes (or second worst, if no one pays the mortgage the property will be foreclosed upon and then all of the heirs will lose).

You are strongly encouraged to get legal advice. While this post is not legal advice specific to any situation I hope the general information helps.