When a person loses their heart, not only do they become a Heartless, what's left of them becomes a Nobody, an empty shell.
Technically, when you stabbed your heart, Kairi's heart was in it. But she didn't had any Darkness in her heart, that's why she didn't became a Heartless. But she still had a Nobody.
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Technically, when you stabbed your heart, Kairi's heart was in it. But she didn't had any Darkness in her heart, that's why she didn't became a Heartless. But she still had a Nobody.