The ownmost possibility is non-relational. Anticipation allows Dasein to understand that that potentiality-for-being in which its ownmost Being is an issue, must be taken over by Dasein alone. Death does not just 'belong' to one's own Dasein in an undifferentiated way; death lays claim to it as an individual Dasein. The non-relational character of death, as understood in anticipation, individualizes Dasein down to itself. This individualizing is a way in which the 'there' is disclosed for existence. It makes manifest that all Being-alongside the things with which we concern ourselves, and all Being-with Others, will fail us when our ownmost potentiality-for-Being is the issue. Dasein can be authentically itself only if it Makes this possible for itself of its own accord. But if concern and solicitude fail us, this does not signify at all that these ways of Dasein have been cut off from its authentically Being-its-Self. As structures essential to Dasein's constitution, these have a share in conditioning the possibility of any existence whatsoever. Dasein is authentically itself only to the extent that, as concernful Being-alongside and solicitous Being-with, it projects itself upon its ownmost potentiality-for-Being rather than upon the possibility of the they-self. The entity which anticipates its non-relational possibility,  is thus forced by that very anticipation into the possibility of taking over from itself its ownmost Being, and doing so of its own accord.
The ownmost, non-relational possibility is not to be outstripped. Being towards this possibility enables Dasein to understand that giving itself up impends for it as the uttermost possibility of its existence. Anticipation, however, unlike inauthentic Being-towards-death, does not evade the fact that death is not to be outstripped; instead, anticipation frees itself for accepting this. When, by anticipation, one becomes free for one's own death, one is liberated from one's lostness in those possibilities which may accidentally thrust themselves upon one; and one is liberated in such a way that for the first time one can authentically understand and choose among the factical possibilities lying ahead of that possibility which is not to be outstripped.1 Anticipation discloses to existence that its uttermost possibility lies in giving itself up, and thus it shatters all one's tenaciousness to whatever existence one has reached. In anticipation, Dasein guards itself against falling back behind itself, or behind the potentiality-for-Being which it has understood. It guards itself against 'becoming too old for its victories' (Nietzsche) . Free for its ownmost possibilities, which are determined by the end and so are understood as finite [endliche], Dasein dispels the danger that it may, by its own finite understanding of existence, fail to recognize that it is getting outstripped by the existence-possibilities of Others, or rather that it may explain these possibilities wrongly and
1 '... die der unüberholbaren vorgelagert sind.' See note 1, p. gog, H. 259 above.