The paper discusses some of the key HCI studies dealing with mortality and death and concludes that the overall research perspective, adopted in most of the studies -- namely, conducting empirical analyses of user practices and trying to improve the practices through iterative cycles of design and evaluation -- is not fully appropriate for understanding the impact of technology on how people experience their own mortality. The paper discusses an alternative research perspective, existential HCI, and argues that adopting that perspective can usefully complement existing studies related to mortality and death. A tentative analysis of "digital afterlife", understood as the persistence of a person's digital possessions and traces beyond the person's life span, from an existential HCI perspective, is presented. Prospects and challenges for future development of an existential perspective in HCI research are discussed.