For starters, I think it's much better to think about phenomena in Buddhism as activities, events or processes rather than things or places. The way it's presented in Theravada, samsara, literally 'wandering on,' is the potential for the arising of human [mental] suffering, while nibbana, literally 'extinguishing,' is the cessation of that potential. As Thanissaro Bhikkhu puts it, "Samsara is a process of creating places, even whole worlds, (this is called becoming) and then wandering through them (this is called birth). Nirvana is the end of this process (emphasis mine)." Nirvana is "realized only when the mind stops defining itself in terms of place ... it's realized through unestablished consciousness."
This may be a bit of nonsense, but in one of the ways I like to look at it, the conventional viewpoint explains things through subject, verb and object whereas the ultimate viewpoint explains things through verb alone. In essence, things are being viewed from the perspective of activities and processes.
This, I think, is incredibly difficult to see, but perhaps what happens here is that once self-identity view (sakkaya-ditthi) is removed, the duality of subject and object is also removed, thereby revealing the level of mere conditional phenomena, i.e., dependent co-arising in action. This mental process is 'seen,' ignorance [of the four noble truths] is replaced by 'knowledge and vision of things as they are' (yatha-bhuta-nana-dassana), and nibbana, then, would be the 'letting go' of what isn't self through the dispassion (viraga) invoked in seeing the inconstant (anicca) and stressful (dukkha) nature of clinging to false refuges that are neither fixed nor stable (anatta). Nibbana isn't the unconditioned as much as it's the unconditioned.
As with all conditional things, since ignorance itself isn't self-sustaining, it persists for only as long as the conditions for its existence persist:
When this is, that is.
From the arising of this comes the arising of that.
When this isn't, that isn't.
From the cessation of this comes the cessation of that.
Thus, by seeing deeply into dependent co-arising [which is synonymous with Nagarjuna's emptiness (shunyata)], we remove the veil of ignorance from our metaphorical eyes and open ourselves to the deathless (amata), or as Dogen says in the Genjokoan, "No trace of realization remains, and this no-trace continues endlessly."
(Incidentally, this kind of reminds me of something I read recently in Bertrand Russell's A History of Western Philosophy. While discussing Heraclitus' doctrine of perpetual flux [which is similar to the Theravadin samsara], he goes to discuss how:
Science, like philosophy, has sought to escape from the doctrine of perpetual flux by finding some permanent substratum amid changing phenomena… Unfortunately it seemed that protons and electrons could meet and explode, forming, not new matter, but a wave of energy spreading through the universe with the velocity of light. Energy had to replace matter as what is permanent. But energy, unlike matter, is not a refinement of the common-sense notion of a "thing" [which can be compared to the notion of selfhood (atta)]; it is merely a characteristic of physical processes (emphasis mine). It might be fancifully identified with the Heraclitean Fire, but it is the burning, not what burns. "What burns" has disappeared from modern physics.
Compare that with what the Buddha says in SN 12.35.)
As for nibbana being the annihilation of consciousness (vinnana) after death, that's how some people interpret the term anupadises-nibbana-dhatu (nibbana element with no fuel remaining) in Iti 44 — as well as the line, "With the cessation of consciousness each is here brought to an end" from DN 11 — but that's certainly not how it's understood by everyone.
In The Mind Like Fire Unbound, for example, Thanissaro Bhikkhu writes that, "This experience of the goal — absolutely unlimited freedom, beyond classification and exclusive of all else — is termed the elemental nibbana property with no 'fuel' remaining (anupadisesa-nibbana-dhatu)." He also points to the term vinnanam-anidassanam (consciousness without feature) in DN 11, and notes that this consciousness, not "partaking the allness of the all," doesn't come under the aggregate of consciousness because it stands outside of space and time. As such, it's a type of awareness that's "not harmed by death."
One objection to this is that consciousness is simply bare awareness of sense data and ideas, and it's absurd to think about consciousness without an object. Positing a transcendent consciousness, then, would be a contradiction in terms. However, this objection is countered by the fact that the consciousness of nibbana is said to have the deathless (amata) as it's object. For example, there's this passage from MN 64:
Whatever is there of material form, feeling, perception, mental formations, and consciousness — he beholds these phenomena as impermanent, suffering, as a disease, a boil, a dart, a misfortune, an affliction, as alien, as decomposing, as empty, as selfless. He turns his mind away from these phenomena; and when he has turned his mind away from them, he focuses his mind on the deathless element [amata-dhatu], thinking: "This is the peaceful, this is the sublime, that is, the stilling of all formations, the relinquishing of the foundations, the destruction of craving, dispassion, cessation, nibbana." (Bodhi)
Moreover, if nibbana were some kind of ultimate (paramattha) or unconditioned (asankhata) reality (dhamma) apart from the conditioned phenomena (sankhata dhamma) of mentality-materiality (nama-rupa), as the orthodox position holds, then it'd at least make logical sense that there could be a seventh class of consciousness outside of the six associated with the sense-doors that 'knows' it. (As a side note, I find surprising parallels between Socrates' dialogue in Plato's Symposium regarding immortality and the idea of forms and the Buddha's discourses regarding the deathless.)
So while some Theravadins describe nibbana as the end of all consciousness, stressing the cessation aspect of nibbana, others describe nibbana as a state of purified awareness and stress its transcendent aspect. To be honest, I can see how both views — i.e., the annihilation of consciousness vs. an awareness untouched by death — seem like the extremes of annihilationism and eternalism. Nevertheless, both have support in the suttas, as well as sophisticated arguments as to why their view doesn't fall into either extreme.
Personally, I used to lean towards the classical position that all consciousness ceases at death, and then I tended to lean more towards the view that there may be a type of consciousness that lies outside of space and time. The imagery of consciousness that "does not land or increase" mentioned in SN 12.64 does seem to support such a possibility, as do various other passages throughout the Canon. And while many assume nibbana to be equivalent to a state of nonexistence, a state of nothingness, Bhikkhu Bodhi points out in In the Buddha's Words: An Anthology of Discourses from the Pali Canon that, "… no text in the Nikayas ever states this. To the contrary, the Nikayas consistently refer to Nibbana by terms that refer to actualities. It is an element (dhatu), a base (ayatana), a reality (dhamma), a state (pada), and so on" (319).
Lately, however, I've been content with viewing nibbana as the extinguishing of greed, hatred and delusion (SN 38.1), and consciousness without feature as the living arahant's consciousness devoid of defilements and non-attached to any phenomena whatsoever, and leaving it at that. In fact, I think Bhikkhu Nanananda sums it up well in "Nibbana Sermon 07":
Now viññāṇaṃ anidassanaṃ is a reference to the nature of the released consciousness of an arahant. It does not reflect anything. To be more precise, it does not reflect a nāma-rūpa, or name-and-form. An ordinary individual sees a nāma-rūpa, when he reflects, which he calls 'I' and 'mine'. It is like the reflection of that dog, which sees its own delusive reflection in the water. A non-arahant, upon reflection, sees name-and-form, which however he mistakes to be his self. With the notion of 'I' and 'mine' he falls into delusion with regard to it. But the arahant's consciousness is an unestablished consciousness.
We have already mentioned in previous sermons about the established consciousness and the unestablished consciousness.[ix] A non-arahant's consciousness is established on name-and-form. The unestablished consciousness is that which is free from name-and-form and is unestablished on name-and-form. The established consciousness, upon reflection, reflects name-and-form, on which it is established, whereas the unestablished consciousness does not find a name-and-form as a reality. The arahant has no attachments or entanglements in regard to name-and-form. In short, it is a sort of penetration of name-and-form, without getting entangled in it. This is how we have to unravel the meaning of the expression anidassana viññāṇa.