I've had the "What about when I die?" thought, too. I don't have concerns about executors having insufficient funds to repay overpayments, it's more a case of how they will negotiate (within UK law) retaining sufficient money in the estate to pay the money back. As I don't have dependents, I can't even think how US-SS would claw back overpayments anyway ... I suppose my executors would be legaly liable to pay my debts, but this isn't really a debt in the traditional sense of the word.
TBH, this is starting to keep me awake at night. As you say, it's not about having the funds to make a repayment, it's the mechanics of doing so. My wife will be having spousal benefit when we choose to take it - although, come to think of it I don't believe that's subject to WEP but could still be overpaid in the event of her death. If she dies before me, and assuming I still have marbles, I'd probably be able to sort out any overpayments although it wouldn't be easy (last resort would be to enlist the help of American friends, who I'm sure would help). In this case it depends how quick they are at stopping benefits once notified of a death (BTW, I see that it's possible to do that online to the FBU) - and current experience tells me they are not quick. As I mentioned somewhere, I am minded to have her benefits paid into a sole account, and even change mine to a sole account (benefit currently goes into our joint) account so that once the account(s) are closed on bereavement, the benefit payments would fail - so they couldn't rack up large overpayments.
If I die before my wife, she is going to have a very difficult time in sorting things out. We still have a joint US bank account from which she/I could write a cheque, but she/I would need to put sufficient funds in there first (possibly be Wise, which she has never used). However, I'm fully expecting one day to be told that they are closing that account because we're non-resident.
Even worse is when we both die and our son(s) have to sort out any overpayments. They don't even have the fallback of a US bank account from which they could write a cheque.
It wouldn't be so bad if I/she/they could haul themselves to the embassy in London and make payments there, but that doesn't seem possible either.
The SSA need to drag themselves into the 21st century. I feel a few pertinent emails to the FBU coming up.