I fear dying, but I do not fear being dead. I'm curious about it though.
Fear is such a basic response to stimuli in our reptilian brains, there is no denying the feeling. Anyone who "feels no fear of death" is merely deluding themselves in one way or another. Yes, you will be afraid at some point before you die about said death. That is part of the process. Especially if the manner of death is particularly painful. Whether or not you express it is a matter of discipline and/or delusion.
I guess you could call a fear of death a fear of pain. We generally fear pain, as a rule. When death would alleviate said pain, people often lose their fear of death, just wishing it would be over with already. You can argue whether this is a cowardly thought or not and whether this is part of a delusion, but I feel no particular way about it.
BEING dead is really nothing to fear for me. If anything, I am curious to see if anything happens. I won't give two hoots what happens after I'm dead when I am dead. Sure, I may give a couple hoots now what happens and, to be sure, I'll try to prepare for that eventuality, but once I actually am dead, everything that makes me me will probably go with me.
At least, that is what present veritable evidence seems to indicate.
To quote Carl Sagan,
"I would love to believe that when I die I will live again, that some thinking, feeling, remembering part of me will continue. But much as I want to believe that, and despite the ancient and worldwide cultural traditions that assert an afterlife, I know of nothing to suggest that it is more than wishful thinking. The world is so exquisite with so much love and moral depth, that there is no reason to deceive ourselves with pretty stories for which there's little good evidence. Far better it seems to me, in our vulnerability, is to look death in the eye and to be grateful every day for the brief but magnificent opportunity that life provides."