What happens to Fox Demon if Naruto dies?

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Chapter 95, page 16 was the earliest mention I could find: If Naruto dies, the Kyuubi dies

Honestly, the Kyuubi sounds more amused that Naruto thinks Kyuubi will die with him than anything else.

If what you're assuming is correct, then a possible last resort action would be ask Naruto to kill himself, destroy the 9 tails, and make the "10 tailed" Eye Hypnosis plan of Madara impossible.

Personally I don't think this question is settled.

Most likely, the Kyuubi will be stuck in limbo for a number of years (longer than the average lifespan of a human), before he is released or at full strength.

That would be the only reason he sees in keeping Naruto alive as profitable, hoping for a chance to break the seal and take over his body.

If demons died with their host, there is no way, after all these years that all 10 demons would be still alive, at least one or two hosts would have died, taking the demons with them, making the creation of the 10 tailed beast impossible.