[This answer is more ambitious than I initially thought. Keep in mind that there are approximations and that they may be more significant than I realize.]
I think that to address your question, we can't avoid delving into the question of death in Sein und Zeit. And in turn, the role of death in SuZ can only become clear once motivated. So, let's start with the beginning and hopefully, by clarifying things along the way, we'll get closer to an answer for your question. Note that I use Stambaugh translation here.
So first, what is the aim and method of SuZ? This is clear from the beginning. The question is that of "the meaning of being (der Sinn von Sein)" and the leading observation is the following.
The meaning of Being must therefore already be available to us in a
certain way. We intimated that we are always already involved in an
understanding of Being.
(Der Sinn von Sein muß uns daher schon in gewisser Weise verfügbar sein. Angedeutet wurde : wir bewegen uns immer schon in einem Seinsverständnis, GA 2, § 2, p. 7)
This understanding can be as simple as the fact that we uses the concept of Being in our everyday life, we can say and understand that "this piece of paper is white". But more fundamentally,
Being [is] that which determines beings as beings, that in terms of which beings have always been understood no matter how they are discussed.
(Sein, das, was Seiendes als Seiendes bestimmt, das, woraufhin Seiendes, mag es wie immer erörtert werden, je schon verstanden ist., Ga 2, § 2, p. 8)
I think this argument more fundamentally draws all of the argumentary of SuZ. Because we say the world populated with beings, it means that as we project the world in front of us and the meaning of the things in it, we also project the Being-ness of the beings with it. (See this answer for more precision on the projection of the world, and this answer for more details on this starting point of SuZ and inherited form Husserl). And so, as the meaning of Being is imprinted on the world by the ourself, if we reconstruct this fundamental way of being-in-the-world (which is one way of understand the da-sein, see the first link), we will, through this reconstruction, give us an access to the meaning of being.
This is very broadly the basic motivation for the existential analytic. (See also this other answer for the very important distinction between existential and existentiell). But which what do we have to put under light the existential structure of the Dasein? Obviously only existentiell observations. Which is why the analytic is initially centred on aspects like "The everyday Being of the 'there'" ("Das alltägliche Sein des Da"). We do not have any kind of direct access to the existential structures of the Dasein, as, at any point in time, it expresses itself ontically.
Now it should be clear enough that this approach cansuffer a fundamental flaw: by trying to infer the existential structure of the dasein through the ontical lense, we don't know how fundamental and structural anything that we learned is. While care appears as the fundamental structure of the Being-in-the-world, that is of Dasein as projected in the world, it is not clear whether it is also the fundamental existential structure of Dasein in general. It could be that the different existentiell expressions of the existential structure of the Dasein that we observed still left a shadow spot on some part of this structure.
This is the difference between a "primordial" and "non-primordial" ontological interpretation.
But a primordial, ontological interpretation requires not only in
general that the hermeneutical situation be secured in conformity with the phenomena, but also the explicit assurance that the totality of the beings taken as its theme have been brought to a fore-having.
(Eine ursprüngliche ontologische Interpretation verlangt aber nicht nur überhaupt eine in phänomenaler Anmessung gesi-cherte hermeneutische Situation, sondern sie muß sich aus-drücklich dessen versichern, ob sie das Ganze des thematischen Seienden in die Vorhabe gebracht hat. GA 2, § 45, p. 308)
(The chapter 45 starts the second part of SuZ and is a very interesting reading as a whole. It really helps, like all chapters beginning a grand chapter or a section, to understand the general articulation of the book.)
And even more precisely, care as the being of the dasein points toward such a non-primordiality:
Care, which forms the totality of the structural whole of Dasein,
obviously contradicts a possible being whole of this being according to its ontological sense. The primary factor of care, "being ahead of itself," however, means that Dasein always exists for the sake of itself. "As long as it is," up until its end, it is related to its potentiality-of-being.
(Der Sorge, welche die Ganzheit des Strukturganzen des Daseins bildet, widerspricht offenbar ihrem ontologischen Sinn nach ein mögliches Ganzsein dieses Seienden. Das primäre Moment der Sorge, das »Sichvorweg«, besagt doch: Dasein existiert je umwillen seiner selbst. »Solange es ist«, bis zu seinem Ende verhält es sich zu seinem Seinkönnen., GA 2, § 46, p. 314)
(Note that I find this passage quite difficult because formulations like "structural whole" often refer to existential characteristics, while here it is somewhat clear that we need to understand it as an existentiell whole. The rest of the chapter 46 hopefully dissipates most of those doubts.)
So, there is a fundamental gap between the existential structure-of-possibilities of the Dasein and it existentiell expression as care, which itself discloses this gap. Care directs the Dasein outward of itself; but this outward is inward the world as projected in front of the Dasein by the Dasein itself. And so the Dasein is in a fundemantal way (e.g. before any state of feeling), in the mode of the care, "ahead of itself".
And this is true, so long as the Dasein lives. When we die, clearly enough, our existential possibilities and their existentiell expression coincide. That is, at the point of our death (and so here, in the existentiell sense), this gap closes itself. Is this the solution to our problem? Not yet. Heidegger writes:
What has been discussed up to now about death can be formulated
in three theses:
- As long as Da-sein is, a not-yet belongs to it, which it will be-what is constantly outstanding.
- The coming-to-its-end of what is not-yet-at-an-end (in which what is outstanding is liquidated with regard to its being) has the character of no-longer-being-there.
- Coming-to-an-end implies a mode of being in which the actual Da-sein absolutely cannot be represented by someone else.
(Das bisher über den Tod Erörterte läßt sich in drei Thesen formulieren : 1. Zum Dasein gehört, solange es ist, ein Noch-nicht, das es sein wird - der ständige Ausstand. 2. Das Zu-seinem-Ende-kommen des je Noch-nicht-zu-Ende-seienden (die seinsmäßige Behebung des Ausstandes) hat den Charakter des Nichtmehrdaseins. 3. Das Zu-Ende-kommen beschließt in sich einen für das jeweilige Dasein schlechthin unvertretbaren Seinsmodus., GA 2, § 48, p. 322)
First point is that which we just saw. Second point is clear enough, the ontical aspect of the existentiell death is that of not-being-the-there. (But § 48 is worth reading too, as things being "clear enough" is very often the root of misinterpretation of Heidegger work.) And the third point is maybe the more delicate.
In this third point, Heidegger uses the negation of the verb "vertreten" which Stambaugh rightly translate by representation. But it is worth specifying that "vetreten" is not representation as mental representation but representation as substitution—e.g. the way an official may "represent" the chief of state.
Indeed, it is important to keep in mind that for the description of the being of dasein as care to be a primordial (ürsprungliche) explanation, there must be—at least—the possibility for the whole existential structure of the dasein to express itself and to appear in the phenomenological dasein—the fore-having (vorhabe) of the excerpt of § 45. The dasein must assume the role of being-all or being whole (ganzsein), as in the excerpt of § 46.
For this reason, this third point definitely shatters any hope that was left. The Dasein, as being-the-there can't represent, as in assuming the role, of not-being-the-there. In the end, this is precisely why death, in the existential analytic, should not bet understood as a yet-to-come existentiell possibility—which is what my comment to Chris was referring too.
And as a matter of fact, Heidegger himself warns the reader against this misinterpretation. (Such warnings are scattered all over his work and those are maybe the most precious pieces of information for the lone reader.)
The end is imminent for Da-sein. Death is not something not yet objectively present, nor the last outstanding
element reduced to a minimum, but rather an imminence.
However, many things can be imminent for Da-sein as being-in-the world. The character of imminence is not in itself distinctive for death. On the contrary, this interpretation could even make us suspect that death would have to be understood in the sense of an imminent event to be encountered in the surrounding world. For example, a thunderstorm can be imminent, remodeling a house, the arrival of a friend, accordingly, being which are objectively present, at hand or Da-sein-with. Imminent death does not have this kind of being.
(Das Ende steht dem Dasein bevor. Der Tod ist kein noch nicht Vorhandenes, nicht der auf ein Mini-mum reduzierte letzte Ausstand, sondern eher ein Bevorstand. Dem Dasein als In-der-Welt-sein kann jedoch Vieles bevor-stehen. Der Charakter des Bevorstandes zeichnet für sich den Tod nicht aus. Im Gegenteil: auch diese Interpretation könnte noch die Vermutung nahelegen, der Tod müßte im Sinne eines bevorstehenden, umweltlich begegnenden Ereignisses verstan-den werden. Bevorstehen kann zum Beispiel ein Gewitter, der Umbau des Hauses, die Ankunft eines Freundes, Seiendes demnach, was vorhanden, zuhanden oder mit-da-ist. Ein Sein dieser Art hat der bevorstehende Tod nicht., GA 2, § 50, pp. 332-333)
Here it is worth noting that Stambaugh translation is somewhat lackluster. "Imminence" is one literal translation of "Bevorstand" but it completely leaves behind the polysemy of bevor (before). Standing before someone may either mine being in front of them, or preceding them in time. And in this polysemy we find precisely the reversal that takes place in all of SuZ and even latter in the Beiträge: the latter something expresses itself phenomenologically, the deeper the existential moment it is the expression of. And so, with this term, Heidegger puts forward the profound existential precedence of death. (The high-quality french translation of Martineau actually uses the term "precedence" to translate Bevorstand).
And so, with death as an existential possibility in mind, what follows begins to make sense:
Death is a possibility of being that Da-sein always has to take upon itself. With death, Da-sein stands before itself in its ownmost potentiality-of-being. In this possibility, Da-sein is concerned about its being-in-the-world absolutely. Its death is the possibility of no-longer-being-able-to-be-there.
When Da-sein is imminent to itself as this possibility, it is completely thrown back upon its ownmost potentiality-of-being.
(Der Tod ist eine Seinsmöglichkeit, die je das Dasein selbst zu übernehmen hat. Mit dem Tod steht sich das Dasein selbst in seinem eigensten Seinkönnen bevor. In dieser Möglichkeit geht es dem Dasein um sein In-der-Welt-sein schlechthin. Sein Tod ist die Möglichkeit des Nicht-mehr-dasein-könnens. Wenn das Dasein als diese Möglichkeit seiner selbst sich bevorsteht, ist es völlig auf sein eigenstes Seinkönnen verwiesen., GA 2, § 50, p. 333)
From there, what is left (sorry for the shortcut) is to show that the existential possibility of the impossibility enables the possibility for the Dasein to be existentielly whole. That, is the show that with it we reach the possibilty of an "authentic Being-toward-Death" (eigentlichen Seins zum Tode in the title of § 53). This is again, a phenomenological investigation carved through the phenomenoligical data of the "everydayness of Dasein", and in particular the "everyday Being-toward-Death" (Alltäglichkeit des Daseins in the title of § 51 and Das alltägliche Sein zum Ende in the title of § 52.)
[This finally gives us all the background we need to answer the question. I'll write the final part friday or in the weekend.]
