No, people should not be afraid to die. Death is a part of the cycle of life, and thus far, 100% of every living thing has eventually died. To be afraid of a certainty is to give that certainty too much power. Instead, people should focus on making the time they have count.
If you lived life to the fullest, why be afraid of death? It is simply something natural that occurs. Death is simply the beginning of a new peaceful life. Some say, when you die, you return as your spirit animal. (Mine is a wolf.) I do personnaly believe that because I believe in spirits and things like that.
To die is a natural process and something that people should not be afraid and of fear of. It is not healthy to live ones life this way in fact it probably will make you even die faster than what would of in the first place. It is best to make the most of your life.