Board Thread:Naruto Discussions/@comment-29965012-20161227225731/@comment-734582-20161228140049

Lorenzo VonMT wrote: Obito didn't willingly end it, kakashi just ran out of chakra. Watch the fight again. Kaguya is defeated, they're all summoned back. Obito talks a bit more to Kakashi and ends the technique. Obito ended it willingly.

Considering Jinchuriki and Edo Tensei die when the thing possessing them is ripped out, Kakashi collapsing is a very mild reaction.