Would all of the guardians perish? Keeping in mind that if the Traveler does indeed "die", it's protection would be gone and everyone would be vulnerable.
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I was under the impression that it had already died while keeping humanity from being wiped out and that the only part of it still functioning was whatever technology it used to maintain flight. You have to wonder who the heck thought that building a city underneath of something that massive, when they weren't even sure how it worked, was a good idea.