They killed his shadow there is no physical manifestation of crota in our world just a shadow of the being in crotas end you go to the hives world (loading seen when you teleport after thralls is to a hive netherrealm likey one of the lowest realms as crota was but a minor god and its in this realm that our fireteams are able to kill him
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So is this why they say the guardians failed to defeat him? It makes a little bit more sense when you pit it that way, but it sounds like they weren't able to best him, and that's why the moon was abandoned. If this is the case however, it makes me wonder... So they beat his shadow at great cost, then gave up after taking out the hive leader? Why? Wouldn't that just be saying, "well, those guardians died in vain."