The man whom the Narrator (Tyler) shot at the hotel was named Patrick Madden, and he was a government official, the “special envoy on recycling.” He was also, according to the Narrator, an enemy of Project Mayhem. He was compiling a list of possible locations of the fight club—and so Tyler killed him. As the Narrator thinks about Madden, it occurs to him that he imagined Tyler in the first place because he loved Marla, and wanted to woo her.
The Narrator begins to see more and more clearly that Project Mayhem’s assassination attempts have become immoral and self-defeating. No good reason for Madden’s death is given—apparently, he just stood in Project Mayhem’s way in some regard. At the same time that the Narrator begins to see clearly what’s wrong with Project Mayhem, he also begins to see clearly why he imagined Tyler in the first place: his affection for Marla.
The Narrator goes to the basement of a local bar, and inside he finds a fight club meeting. Everyone greets him with great respect. He proceeds to fight with many of the members, and bleeds copiously. As he fights, he pictures Patrick Madden’s wife kneeling next to her husband’s dead body. The Narrator pushes through the pain and continues fighting—“Only in death,” he thinks, “are we no longer part of Project Mayhem.”
In this passage, the Narrator tries to use pain and violence for different purposes than he has previously. By fighting, the Narrator seems to be punishing himself for Madden’s death (and for the emotional pain he’s caused to Madden’s loved ones, such as his wife). He atones for his crimes by allowing himself to bleed (not that this actually helps Madden’s family in any way, however). Death, he now believes, is the only escape from the guilt he feels for leading Project Mayhem as Tyler. His statement also seems to suggest that “Project Mayhem” has grown so large as to encompass life itself—the universe as a whole is violent, meaningless, and cruel.