Kabr didn't die. Read the description on the Battlecage of Kabr.
English
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Kabr died in order to give the Aegis its power in order to make the vault possible for other gaurdians, I would assume that the templar was put in to gaurd the vault after kabrs 2 attempts.
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He didn't die. He gave his light for the aegis
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read the bottom of my post i went into more discription on the notion, but i didnt do it at first because i thought it was pretty obvious how both Preadyth and Kabr died.
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it could be that kabr went in once by himself, but by the text "No one can open the Vault alone. I opened the Vault. There was no one with me but I was not alone." it could mean that he had a fireteam before this one, or that hes talking about the vex.
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This could also refer to when Kabr was melding himself with Vex armaments.