Neither Linda nor John can manage the transition from the Indian Reservation to the brave new world. Linda has done nothing but dream of returning to "civilization," but once she arrives, it is impossible for her to fit in once again. First, her looks repulse people used to a culture in which everyone is young and fit. She is fat, old, her teeth are bad and her complexion is blotched. People feel sick looking at her. She is also embarrassing because she has given birth to a child, which is considered obscene (children are supposed to be grown from a test tube in a lab). People avoid her—and that is fine with Linda. As the book explains:

The return to civilization was for her the return to soma, was the possibility of lying in bed and taking holiday after holiday, without ever having to come back to a headache or a fit of vomiting, without ever being made to feel as you always felt after peyotl, as though you’d done something so shamefully anti- social that you could never hold up your head again. Soma played none of these unpleasant tricks. The holiday it gave was perfect and, if the morning after was disagreeable, it was so, not intrinsically, but only by comparison with the joys of the holiday. The remedy was to make the holiday continuous. Greedily she clamoured for ever larger, ever more frequent doses. Dr. Shaw at first demurred; then let her have what she wanted. She took as much as twenty grammes a day.

Although the doctor knows this will quickly kill her, he allows her the large soma doses anyway, saying it is impossible to "rejuvenate" her.

John objects to this suicide/euthanasia as "not right," but he can do nothing about it.

John also finds it impossible to fit into this new world. Although Linda has told him nothing but glowing stories about it all his life, when he gets there, he finds it vapid and sterile. Its morality is completely alien to him (he can't, for example, understand the lack of sexual fidelity in this society). He has imbibed the religious faith of the Indians, a hybrid of native practices and Christianity with an emphasis on suffering and redemption. He has brought himself up on Shakespeare and now is faced with a world without any real poetry or art, without religion, without challenges, without any need for heroism or self-sacrifice. On top of it, he is treated like a sideshow freak and can never get any privacy. In the end, it is too much, and he commits suicide by hanging himself. 

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.