I don't really get this question. If you believe that there is no consciousness in death, then there is nothing to 'deal' with when you are dead. Moreover, since it is not possible to really conceive of non-existent consciousness, there is nothing scary that you can imagine about it when you are alive. It makes more sense to ask how people who believe in eternal life deal with the permanence of life, since that is something you would actually have to experience.
Maybe you meant to say "how do you deal with the impermanence of life?" Well, life's stages are full of impermanence - the impermanence of childhood, the impermanence of beauty, the impermanence of love. Impermanence is one of the main things we celebrate in life.
I feel that you're focusing too much on semantics. My intent was to encompass both ideas, the reality that life is impermanent and that death is the unavoidable finality, and how we live and cope with those concepts.
Both your comment and that thread were very interesting reads. I've enjoyed some healthy debates over religion, but heaven has always been a topic that I've never felt comfortable "taking off the gloves" to discuss with a person of faith. Partly because I empathize with their need to believe a comforting lie and also because - unlike the topics of evolution, earth's age, the creation of the universe, and abortion - I'm okay with people deciding on an explanation that suits their emotional needs.