She met him when she has chosen to stop living. He met her when he was struggling to keep living. Hazel was sure that ending her life will end everything, her longing, her pain and her nothingness. So, she keeps trying, to end her life. Being so young, Brian received a death sentence. He was no longer able to participate in a lot of things, afraid that it will lead to his death. But, he keeps trying, to stay alive.