According to the ancient Brahmans, when a fire was extinguished it went into a state of latency. Rather than ceasing to exist, it became dormant and in that state -- unbound from any particular fuel -- it became diffused throughout the cosmos. When the Buddha used the image to explain nibbana to the Indian Brahmans of his day, he bypassed the question of whether an extinguished fire continues to exist or not, and focused instead on the impossibility of defining a fire that doesn't burn: thus his statement that the person who has gone totally "out" can't be described.
However, when teaching his own disciples, the Buddha used nibbana more as an image of freedom. Apparently, all Indians at the time saw burning fire as agitated, dependent, and trapped, both clinging and being stuck to its fuel as it burned. To ignite a fire, one had to "seize" it. When fire let go of its fuel, it was "freed," released from its agitation, dependence, and entrapment -- calm and unconfined. This is why Pali poetry repeatedly uses the image of extinguished fire as a metaphor for freedom. In fact, this metaphor is part of a pattern of fire imagery that involves two other related terms as well. Upadana, or clinging, also refers to the sustenance a fire takes from its fuel. Khandha means not only one of the five "heaps" (form, feeling, perception, thought processes, and consciousness) that define all conditioned experience, but also the trunk of a tree. Just as fire goes out when it stops clinging and taking sustenance from wood, so the mind is freed when it stops clinging to the khandhas.
Thus the image underlying nibbana is one of freedom. The Pali commentaries support this point by tracing the word nibbana to its verbal root, which means "unbinding." What kind of unbinding? The texts describe two levels. One is the unbinding in this lifetime, symbolized by a fire that has gone out but whose embers are still warm. This stands for the enlightened arahant, who is conscious of sights and sounds, sensitive to pleasure and pain, but freed from passion, aversion, and delusion. The second level of unbinding, symbolized by a fire so totally out that its embers have grown cold, is what the arahant experiences after this life. All input from the senses cools away and he/she is totally freed from even the subtlest stresses and limitations of existence in space and time.
The Buddha insists that this level is indescribable, even in terms of existence or nonexistence, because words work only for things that have limits. All he really says about it -- apart from images and metaphors -- is that one can have foretastes of the experience in this lifetime, and that it's the ultimate happiness, something truly worth knowing.
So the next time you watch a fire going out, see it not as a case of annihilation, but as a lesson in how freedom is to be found in letting go.