The nine-tails would die if Naruto died... at the point where Naruto summoed gama, the conversation with the nine-tails went somewhere along the lines of...
"Give me some of your chakra!" - naruto
"Hmm, so if you die, then I will die... quite a way to blackmail" - nine tails.

I think the reason the fourth sealed it in Naruto, even though he could have sealed it in himself, will be revealed in a later plot twist.