It sounds like the lien is on the decedent’s estate, not actually owed by the heirs.
In NJ, a man I knew was abused by his father and moved away at 18. Thirty years later, his estranged father died after several stunts in prison and then nursing home. Hadn’t seen each other for decades.
He got a bill from NJ for hundreds of thousands of dollars of care because they do, indeed, have a law making the children responsible for the debts of the parents.
How, in all this world, is that even legal.?
I can see where they might go after anything with the parents name on it but, beyond that, (??)