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Nooo, they can't die. D: They just can't! BOHOO!

How 'bout... They'll become Nobodies of some other fellows? Like, when a strong-hearted dude loses his heart so powerful Nobody is born and it takes a humanform and it'll look like and have same abilities than for ex. Saïx but has just different name? <:'D Guh.

That sounded stupid.. But that may be! D:

Bless meh great theories! :'DD I'm just desperate. XD

But they do not die. D: I'll make up some other stupid theory.

I wouldn't say they die. They are only the body left over from a heartless person. Remember? When an individual loses their heart, a nobody is created, but if the person had a strong will- their body, the leftover shell carries on with the will of the individual.
The body can be broken, but without a heart, could it really live to begin with? I think Nobodies can only die once the heart is returned. Untill then, broken bodies are returned to the darkness and nothingness from whence they came untill the bodies will causes it to rise again. If a person's will can carry on without a heart, what makes you think it will die?

Well I get this weird impression that they don't really die because of two hints:

{SPOILER on the second half.}

One was from the KHII game itself. After you finally infiltrate the Organization XIII's hideout, and beat a few of the members, you reach a certain room that contains the members' "graves". If you look carefully around the room and the way that it is designed, there are these strange looking vines that course their way from the tombs to the final doorway at the other side of the room.

Even more bizarre than that is the fact that they eerily pulsate some odd glowing substance from these graves to the doorway.

This specific scene seems to have a connection to one of the secret clips in the final mix (or one of the other sets of secret editions that were sent from Japan.) When Xemnas enters the same area where Tron's world is, there is a secret basement that apparently only he is capable of entering. There could be others who could do that, but right now he is the only known one with access to it.

Anyway, once he goes down into the secret basement, he passes through a hallway full of dungeon like rooms. Looking more carefully you see that they are all chained, contain some kind of computer-like keyboard, and so on and so forth. There seems to be quite a lot, possibly a certain number of them. They all seem to connect once again to the final room at the end where Xemnas greets a pile of armor who he calls his "old friend".

All these I feel have a connection to the Organization XIII members, why they are there, what happens to them when they "die", and the true purpose of that room called "Proof of Existence". The way each member reacted to their "deaths" is somewhat vague, but you can be sure from the ones like Demyx that they are receive a fate much worse than death.

...no...and hello everyone! n_n

That would be Ven, Aqua, and Terra.

nobodies cant truly die
they would just fade back to Castle Oblivion