I started a thread on this some weeks ago, as my twin 9 yr olds often say - usually last thing at night - what would I do if you died, mummy and get so upset, they get tearful.
On the one hand, I think this might well be a phase, as they reach a developmental age when they realise that death happens and what it really means.
On the other hand, it could also be because my twins have only me at all in their lives and my parents - their only grandparents - have died over the last 5 yrs.
My response differs depending on the mood of the moment but these are some things I say: Yes, we all die and if we didn't we'd never have lives. So being able to die is actually a natural part of life and if you don't die, it means you never lived (that one's for the calmer, rational moments)....or...look, do I really look like I'm going to die any time soon? I'm bursting with life! I haven't got time to die! (if it's a jovial moment)
...or....Hey, of course one day wehn you're much much older, I may die and like me, when my parents died, you'll be very sad and cry - but as you've also seen with me - my life goes on and I'm v v happy because I've got lots of lovely things in my life - most of all you two. So I'm a good example of how people can lose parents and be sad but also still live and be happy....
...or...Enough of that. Let's think and talk about what good stuff is happening tomorrow/ what happened today...etc etc - and get them to describe in detail something positive...
My worst fear of course is that I WILL die before they've fully grown and got a full life of their own. But I suppose this must be everyone's fear and as a parent, my task is to model managing the fear of death, despite feeling the fear and resistance to it.
Don't necessarily conclude your DC is anything other than having a normal phase at present. Children go through lots of different phases and come out the other side and are fine. I think of you try not to show your own concern about their fear and upset, that this will help - otherwise they play on your emotions.
My twins currently have a'joke' going on in that every single time I say something they don't like eg "No you can't have a snack before lunch", they say, "I'm going to commit suicide!" Yes, I freaked out when they first came out with this but now we laugh about it and then they model their teddy bears committing suicide by jumping off the end of the bed, when the other bear punches it and then they laugh too.
they know this is playing and they also know that it'd be something completely different and v serious if someone really means this. So I give them credit to know the difference and don't take it to heart, despite sometimes worrying inside me what if they continue using this threat in adolescence, when I think I'd respond differently - unless they were also using it to wind me up!