If you listen closely to your ghost at the end of that mission he says that the sword disappeared and was not destroyed. I assume Crota called it back to him after he noticed us using it.
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What's to say these events dont happen in the order we play them?
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Well also we KILL CROTAS SOUL IN THE LAST MISSION FOR CHRIST SAKE! How is he still alive!?!?
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We don't kill his soul!! We destroy the crystal that holds his soul, his soul is just banished from our world back to the world where the Raid exists.
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No he says "It's gone", not that it's disappeared.
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But at the beginning it says the swarm princes keep it "alive"(for lack of a better word)