Okay but without strife there's no pulse l'cie to cause that to happen. It doesn't and won't just fall on its own.
Did you even play XIII-2, the pillar keeping it aloft wears down eventually, you stop one paradox that was eroding it and made it collapse by 400 AF, but the paradox being resolved only delayed the collapse until 500 AF. And in the good 400 AF with Hope leading it, they still knew that Cocoon would collapse eventually so they were making plans to create an artificial Cocoon that they would raise into the sky so that humanity could be saved.
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tfw no big tiddy goth vampire gf who lactates blood - viewmaster_pi