The connection between death and the individual existence is a key element in Heidegger’s work. Indeed, while he does not aim so much to assuage our fear of death, Heidegger does have a positive conception of death as it stands in relation to individual existence. Death is, according to Heidegger, our “ownmost possibility” and one way of explaining this is to say that no one can die my death for me. What is an issue here does don’t concern any mere point of grammar, nor is it to do with ownership or failure of substitution. Instead it concerns the way in which my death marks out my life as my own, as life for which I must “own up”, whose possibilities are my possibilities, and so define and constitute me. In this respect, Heidegger’s emphasis on the “ownmost” character of death connects directly with what I have termed the strangeness or unrepresentability of death, which concerns the way in which death marks out my life as my own even while it also marks the limit of that life.From "The discomfort of strangeness", The Philosophers' Magazine 27.
Yet if death is tied to individual existence in such a way that doing away with the self does away with death, then it also the case that doing away with death does away with the self? On Heidegger’s account, this conclusion would seem to be inevitable. Heidegger understood death in existential-ontological terms, which is to say that he takes to be that which makes possible (“constitutes”) the existence of the self whose death it is. This means that without death, there can be no self, no individual existence. The claim that death may actually be a requirement of the possibility of individual existence is not only to be found in Heidegger. It also appears in the works of other existential thinkers, notably in Camus and de Beauvoir (but not, significantly, in Sartre), as well as in Bernard Williams.