Extraposed clauses

"Before the war, you always think that it's not you that dies." - Ernest Hemmingway

I'm having trouble diagramming this sentence. My question is about the subordinate clause in bold. Is the extraposed that-clause("that dies") at the end the subject or an adjective of the subject?

When you un-extrapose it, would it be : "that it that dies is not you" or " that that(who) dies is not you."?

The first "that" is a complementizer which converts the following sentence into a nominal. This nominal is the object of "think".

Before the war, you always think [NP that S].

The S is a cleft sentence: "It's not you that dies." It's not really clear what the structure of cleft sentences is, but clearly "that dies" is a relative clause. See McCawley's The Syntactic Phenomena of English for a discussion of the structure of clefts, or the Wikipedia entry for Cleft Sentence.