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They may have a formerly human consciousness, but that doesn't make them human. In the ven diagram of what humans and exos share, a soul is the only item. Even that can be debated. We do know some exos were originally human, however we don't know if that is the case for every exo.
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From my understanding they are human consciousness out into an Exo body after they are killed or sowmthing. Also the number after their name is how many times the memory has been wiped So cayde 6 has been wiped 6 times to be who he is now