I think many people are afraid of death because they confuse death with non-existence.
That kind of thinking is, in my opinion, based upon a misconception about the nature of our existence.
I remember saying to my brother once, when we were talking about such topics, that it's not possible for us to die because we were never born to begin with.
What we consider being born in the practical sense of the term (i.e. coming out of our mother's womb) is in reality just a change in our existence. We, the atoms that compose our body, were already in existence prior to our "being born". Not as a person perhaps, but as something else entirely. Stars, earth, who knows.
What I mean to say is that we came into being when the universe itself came to being. Now whether that happened at the time of the big bang or the universe is actually a series of cycles I have no way of knowing and, I think, nobody has.
So, when we get old and die, it's just a slight (very slight indeed, from the perspective of the whole universe) change in out nature, it's nothing to worry about.
Our existence is tantamount to the universe's and I have a feeling that the universe's existence stretches back to negative infinity and will, in the same measure, continue to exist up to positive infinity. This is just another way of saying that the universe has always existed and will always exist. Since we are the universe itself, it follows logically that we have also always existed and will also exist forever.
This is why I think there's nothing to be feared. Death is not the same as non-existence. I don't think anyone could truly cease to exist even if they really tried.
P.S.: sorry if this seems a little far-fetched for you. I don't claim to be right, it's just a personal opinion.