Same as when everyone else disappears, probably. Maybe more, because you will literally live on metaphorically in Sora. Most people when they die, they die, they rot and become dust, they most they can do is leave some sort of legacy on their kids but that's not the same.

[Ikki closes his eyes and frowns before he looks at Roxas.]

Listen, I don't know what ideas you have of "heart" people, but let me tell you something. No one gets to exist because they asked for it. No one asks to be alive, and many people are born without being wanted or expected. Many "heart" people are people that "shouldn't exist", but they do, and they are normally given the shittiest options available to live on.

The difference between you and them is that you, as much as you "shouldn't exist", have a purpose. A reason to be. Yes, that reason basically is that you have to vanish so someone else can go on. But normally people don't have even that. They are thrown into life without being asked about it, forced to live a life that they may very well not want or like, and then they die and in a matter of a few years they are forgotten, and any traces of their existence get erased long before even that happens.