How do you get over the depression?, more like, how do you get over being scared of death or dying someday?
Psychotherapy. It is likely that the known fear, of death or dying, is actually masking an unknown fear that seems worse. The purpose of psychotherapy is to uncover the unknown fear so you no longer use fear of dying to cover it up. The good news is that the unknown fear is probably something that the child was afraid of and that the adult would not be afraid of.
Psychotherapy. There is no answer to this question that fits every person. Generically, i would submit that the fear of death doesn't ever completely go away. How we react to these fears and concerns probably has the most relevance for living day to day though. For many, this fear and reality that we all will die instills a sense of urgency to live their lives with the most value and meaning possible.