This type of anxiety is a part of the human condition, and it explains the appeal of many religions to the human condition as it offers some relief from the anxiety about our life ending.
Either I'm not human, or such anxiety isn't really part of the human condition. I can't care less about the fact that I will die one day. I don't dread my existence. I don't worry about the fact that life is fragile and can end at any moment. If it's going to happen, it's going to happen. I have no control over it, so why worry? I am aware of it, but that's all I have, awareness, not anxiety or dread.