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Would Shadows Selves be eligible for the Immortality trope? Unlike other Shadows (which are fragments of mentality, apparently) it doesn't seem possible to kill them. You can beat one down and revert it to its base form. You can accept it and change it into a Pesona, but even then, it's not gone, and there's implications that a Persona can turn back into a Shadow. The only time a Shadow ceased to exist was when Mitsuo Kubo became so absorbed by his own worst traits that it was no longer distinct from the real thing.
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How well does it match the trope?