The postmodern breakthrough revealed the limitations of history understood as the dominant approach to the past, but it does not follow that history should be abandoned. We might wish, rather, to try to seek an alternative to history, or at least a supplement to it. The search for such an alternative could begin on the border between archaeology and history, where the status of material culture and historical sources can be investigated. Contemporary Heideggerian or contemplative archaeology suggests the possibility of abandoning textualism and turning to questions of the past's materiality. For the historian, the Heideggeran approach encourages the rethinking of the historical source, considered as the trace-being and trace-Being, as well as changing the repertoire of questions. As a case in point, I reflect on the dead body and various aspects of its existence. Analyzing the case of the Argentinian desaparecidos, I discuss the dead body as evidence of crime, as an object of mourning (trace-being), and as the absent remains which refer to the unpresentable 'absolute past' (trace-Being). I situate the dead body's existence in the space of the non-absent past, whose ambivalent and liminal status protects it against the all-encompassing discourses of the living. In the context of those considerations, prompted by Heideggerian archaeology, I try to demonstrate that thinking in terms of the non-absent past and turning to the issue of 'the ontology of the ashes' may open up the possibility of a reflection on the past which turns to a- or non-historical approaches and whose reference point is the future-to-come.