In the most basic of terms, Louis Zamperini does not break. He withstands all of the pressure placed upon him and he never breaks. He is put under the most intense of forces in the most brutal of situations. He is physically, intellectually, emotionally, and psychologically tested. Forged through such trials, he does not break. He is unbroken. He withstands the challenges placed upon him. The title is a reflection of his characterization throughout an ordeal which would have broken many others.
Given how Hillenbrand develops his narrative, it becomes evident how Louis Zamperini had always remained "unbroken." He fights through adversity and challenges throughout his life. Zamperini represents the essence of toughness and a steely will that enables him to endure most anything. The adversity of distance running does not break him, nor does the loss of his dream competing in the Olympic games. His work as a fighter pilot tests him, but he never capitulates as he shows success in this realm, as well. Being shot out of an airplane, surrounded by sharks and swimming for his life did not break him. Being a prisoner of war on "Execution Island" failed to break him, as well. The abuse Louie suffered as "prisoner number one" is gruesome and brutal. However, his resolve did not break. The emotional challenges of both returning to civilian life and having to confront health issues that endangered his chances of running again also failed to break him. In the end, his endurance and strength to simply persevere is what makes him "unbroken."
When examining the title of the work, I feel that it is a direct reflection of the main character. Describing all that Louie endured and the challenges he faced and being able to say that he remained "unbroken" from them represents an act of strength in mere verbal articulation. To have experienced such a reality enables the individual to grasp why Hillenbrand chose such a descriptor to fit Louie and the life he led.