I thought the white vapour that appears when you head shot them was their souls being torn from their body.
English
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To quote the kellbreaker's gloves: "The gas is no soul. An ethereal lifeblood, perhaps, but a soul? I think not."
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There are a few sources that might agree with you there, but as far as we know the Fallen don't have any supernatural powers like the Guardians or the Hive, so it always felt odd for them to have such a ethereal trait. I try to explain it with pure science.