I don't know how AMEX handles it, but Delta transfers points. When I mother passed, I was the executor of the estate. My brother agreed that I should have the points since I could use them to buy tickets for my honeymoon in a few months (yeah, it sucks not to have a single living parent when you get married at 30).

I called Delta, and that happily transferred the points to my account. I had to fill out some quick form.

Since points have value, if you were either the executor or a beneficiary, and transferred points, you could wind up in trouble if anyone else that is a potential beneficiary finds out you took points out.

Oh, and one point to mention. NEVER ASSUME RESPONSIBILITY FOR THE DEBT. NEVER. You tell them you will not assume the debt, and debt resolution will be handled by the estate.