Adam Buben on the common sense of death in Kierkegaard and Heidegger.
It is their shared concern about the chronologically accidental and interest in avoiding it that leads both Kierkegaard and Heidegger to describe this process (of avoiding it) in terms of death. Physical death, while not ultimately what they are focused upon, provides an important “formal indication” of essential features of human existence and a deeper sense of dying. For both Kierkegaard and Heidegger there is no other occasion that better demonstrates the contingency of all attachments to and ways of understanding one’s place in the world; the image of death is employed because it is the best way to awaken someone from the complacent slumber of a thoughtless existence (e.g. as a merely cultural Christian, or a “they”-self) that is not essentially and necessarily theirs. That one will die signifies that existence has to be given up one way or another, and realizing this already has a way of weakening the bonds of meaning that are passed down to us merely by existing in the world. But what is more, the uncertainty with regard to the when of physical demise suggests a general indefiniteness in existence, particularly in connection with worldly endeavors and understanding. Given this structural indefiniteness one need not feel constrained to interpret existence strictly as a function of the specific projects, relationships, and goals that the everyday world recommends. Without such constraints, both Kierkegaard and Heidegger believe that it is possible to appropriate meaning for oneself in the light of one’s contingent, and admittedly culturally-textured, situation.
From "The Perils of Overcoming 'Worldliness' in Kierkegaard and Heidegger