Linda dies from an overdose of soma which is fitting considering she is like John and really doesn't fit in anywhere. Linda subscribes to the ideas and soma use of the BNW and seems to use soma to dull her perception and awareness of her existence.
John dies for entirely different reasons. John commits suicide because it is the final act of choice that he can exert on a world that he does not accept. John refuses to accept anything about the BNW and since he does not really fit into the savage reservation also, he decides to commit suicide.