I mean, it makes sense (to me at least) that spouses would inherit debt "that was their spouses", with the possible exception of established prenuptial/last will and testament agreements creating a grey area in favor of the surviving spouse.
By default, a marriage is a merging of finances and households.
Without things like prenups and wills, a divorce is going to be a process of splitting all liabilities and assets 50/50. Similarly, without prenups and wills, the surviving spouse is going to inherit all of assets AND all liabilities (because technically they always held them in tandem with their spouse).
Now, if there was always a prenup, Hubby always had the money, Wifey was on a weekly/monthly allowance, and Hubby had a will where he left all the money to his son from another woman, leaving Wifey with nothing, Wifey didn't get any assets, obviously she doesn't inherit any debt.
Outside marriage, I think it should go like this:
Upon death, non-liquid assets get distributed. Timmy inherits the Pontiac GT, Harriet inherits all of the clothes, Wilfred gets all the furniture, Freddy gets the house. Any SECURED liability on the non-liquid assets stay attached. Dad had 3k left on the car loan for the Pontiac, Timmy can take over that car loan. If Freddy doesn't want Dad's house worth 300k dollars with 200k left on the mortgage, he has the option to liquidate the house, but the proceeds from that sale go into the liquid assets of the estate, not into Freddy's pocket.
After non-liquid assets have been distributed/liquidated and BEFORE any liquid assets get distributed as inheritance, liability holders for the estate get to fight over what ever liquid assets are there. If the estate, after liquidation, has 400k in liquid assets, secured liability holders (the mortgage company) are going to get first stab at the money. The mortgage company recovers its 300k. Then any unsecured liability holders (Dad's credit card he ran up to 60k dollars) get next stab at the liquid assets. They recover their 60k, that leaves 40k in liquid assets.
If the liability of the estate exceeds the liquid assets of the estate, no dollars are going to anyone in the family. Liability holders get all the money, and some of them probably get stiffed on the remainder.
In no event does unsecured liability get shuffled off on a successor of the deceased.
If there are no liquid assets left after liability has been resolved, Frankie doesn't get the 10k Dad's will said was bequeathed to him.
No idea how all of this actually plays out. Just my opinion on what should happen with an estate after death.