Talk about the feelings, whatever they are. She’s afraid of dying…ok. What about dying scares her? Is she afraid of not existing? Or is she afraid she won’t have accomplished as much as she wanted to?
If she’s not a believer, then she wouldn’t be worried about “afterlife.” Or would she? Some people say they don’t believe, but they still worry. So talk about that. Maybe she’s questioning her beliefs. Or not. Get her to talk more about that.
A decade ago I had a breast cancer scare because of a bad mammogram & I had to wait 6 months for another ultrasound check. During that time I was really scared. But I asked myself, if I were to die now, what would I most regret not having done? Mine were: 1] completing my dissertation; 2] spending more time with my daughter and grandchildren. Then I set about accomplishing tasks toward those two goals.
By the time the second ultrasound came around I’d been happily working toward my goals little by little. And the scan was fine.
Give her something to occupy her mind to take it off worrying about dying. But let her pick what it is.