So she already had two personalities from the beginning? Or she started dissociating due to trauma from almost dying? At least I don't think she's possessed yet, her situation is nowhere as bad as Lust dude for that to happen yet, she's also seemingly aware of her other self too.
Possessed by the spirit of her dead twin that was stillborn maybe? Could explain why her being Greed seemingly works different from Lust dude.
Honestly, give me any asspull as long as it justifies Reaper survival lol