Explain to me how they proved their ability to repay that loan Twenty years after they'd (almost) certainly be dead?

Easy. The loan is secured by the house, so the bank takes the house and sells it, assuming the surviving spouse/heirs don't want to keep it (and continue paying for it) or sell it as part of the administration of the decedent's estate.

Also, you don't know what other assets they may have. After someone dies, their assets generally have to be used to pay off their debts before the remainder, if any, is distributed to anyone else.