I agree it is right and just for a person who paid the rightful debts of the estate to get reimbursed. (Actually, indemnification/contribution.)
But, the facts get fuzzy real fast. For example, if the OP (husband) was the only one on the suit he defaulted upon, who's to say it is the estate's debt? What of mitigation or the right to be heard? The estate has rights to challenge the debt if it is supposed to pay it. And, even if it is a mitigated estate debt, does it maintain the character of the underlying claim (Here, we're *assuming* some debt related to nursing home.), or is it an after-acquired debt? That is important because of the order of payments and if there is enough in the estate to pay it off. Many more issues too.
That's why I like the way anteater phrased it:
Still, if the heirs are reasonable and don't "go all technical" (if the question of liability for the unpaid bill is at all muddy), it should be possible to have the probate estate pay the claim.
If it gets to technical, there will be problems. If everyone just agrees and moves along as one big happy family, with the exception that the court will have to approve payment of a debt to the OP(h) if he is also the administrator, it might work out.
But, nothing is going to clear up the lien on the house for a while.