Fear of death, no. Concerns of the unknown method of death, yes. Death is part of a natural progression.
In my last brush with death I was almost irrationally calm, I knew what might happen, I even had talks with people that I didn't expect to make it through, I wasn't in any way afraid of my time being up. That doesn't mean I ripped any tubes or I.V. limes out, just that I was ready if that was to be.
My bigger concern at the time was the milk in my refrigerator which was going to go bad, I asked a friend to get that out of there, which he did.
Milk going sour....terrible!
Death...well, it has to happen sometime, no need getting worked up over it.
Besides which, what if it turns out we're already dead and we're just getting ready to live?