It's probably not something you tend to think about. You're divorced now right? But if your kids are next of kin and your ex has not made other provisions, nor has parents around, you may find yourself dealing with the estate.
Having an ex die may affect you in ways you can't imagine. Think back to Cher giving a eulogy at Sonny Bono's funeral. She was sobbing and could hardly speak. I have a friend who just lost her ex husband and though she is even remarried, she has hardly had a day go by for weeks when she didn't break down.
Just because you aren't married doesn't necessarily mean your connection is over. And certainly if you have kids, it is not easy to watch your kids lose someone that they adore. So though you may be divorced, the death of your ex spouse may touch you. It might be wise to discuss with your ex if there should be provisions or a will in case they die a premature death.
I know my ex and I are pretty good friends, and I can't really imagine anyone else at this point handling my affairs, especailly since it would be on my kids behalf. But you may not have that kind of relationship, nor trust, so it's wise that you think about it and have that conversation sooner rather than later.