The Stranger ends on the night before Meursault is to be executed for the killing of the Arab man on the beach, so it can be assumed that he does indeed die—just not within the text itself.
Camus implies that Meursault is being executed for more than just committing murder. The members of the court appear more horrified by Meursault's lack of tears at his mother's funeral than they are by his act of violence. Even before the trial, Meursault's lawyer is shocked and appalled by his client's lack of emotion.
The trial goes badly for Meursault because he does not hide his indifference toward life behind false sentimentality or feigned emotions. While his lawyer tries making an argument for why Meursault behaved as he did, Meursault does not go with this line of thinking. While being questioned before the trial, Meursault's lack of willingness to ascribe meaning to his actions is apparent:
"Why did you pause between the first and second shot?"
I seemed to see it hovering again before my eyes, the red glow of the beach, and to feel that fiery breath on my cheeks—and, this time, I made no answer.
During the silence that followed, the magistrate kept fidgeting, running his fingers through his hair, half rising, then sitting down again. Finally, planting his elbows on the desk, he bent toward me with a queer expression.
"But why, why did you go on firing at a prostrate man?"
Again I found nothing to reply.
Camus has called this a case of Meursault refusing to "play the game"—that is, refusing to impose order on an illogical universe. He accepts that sometimes life makes no sense and that events, both bad and good, can occur for no reason at all. This idea is threatening to the social order, which demands that all life have a cause and effect or that people order their lives according to a moral system, such as the law or religion. When Meursault refuses to do so, he loses the sympathy of the court and effectively signs his own death warrant.