My condolences to those FT members that have lost loved ones. I have been thru this twice, once helping my father receive my mother's SkyMiles when she passed away (pretty straightforward transfer to surviving spouse and well-covered in previous posts).
I also went thru this when my life partner passed away. Since we were not related legally, DL obviously asked for more documentation. However, he had SPECIFICALLY listed his SkyMiles in his will. A copy of the will, a certified copy of the death certificate (yes, you can never have too many of those), and some nice folks at DL got it all worked out. I should add that, as the surviving half of a gay couple, I received nothing but professional treatment, respect and courtesy from DL. This was one of those times when everything did work the way that it should.