Macrophages sweep up cellular debris and pathogens in order to thwart infection - sometimes even before the white blood cells, which are designed for that task.
Neutrophils, white blood cells, are "first responders" that are attracted to wounds by signaling molecules called reactive oxygen species (ROS) that activate a protein kinase. When neutrophils finish their work, inflammation is partly resolved through apoptosis, or cell suicide, and then macrophages arrive to clean up the infection.
But neutrophils can also elect to leave wounded tissue in a process known as reverse migration. Whether macrophages promote this mode of inflammation resolution is unclear.