It is pretty much a given that all people at some point question their mortality and worry about death.
In the local supermarket this afternoon I was "witnessed" too by a missionary. I guess his assignment after service was to hit up the market for converts. After his usual pitch, I asked him if he was scared to die. Of course he said no. He was in the great number of saints. Then I asked him what if he died and there was no immortal existence, and all of the missionary work pointed to a great nothing? He looked upset and said, then I would have wasted my life.
I calmly said, I rest my case. Smiled and before I walked off, I told him death is nothing to us. We have no recall of life before birth. Death is the same way. No sensation. Don't fear it. Live today.