Henry Cornelius Brown Jr., brandishing two handguns, kneeled down outside a police station in Shelby, South Carolina, in 1997 and begged police to shoot him. Feeling that Brown posed a threat to their lives, the officers opened fire, killing him. Brown thus became another casualty in the phenomenon known as “suicide by cop.”

Experts believe that 10 percent of the roughly six hundred fatal shootings a year by law enforcement are the result of people provoking police in a desire to end their own lives. Often, these shootings prompt charges of police brutality by the community. Those who incite police to kill them are mostly men in their twenties with drug or alcohol problems. As Alan Feuer, reporter for the New York Times, reports, most people who want police to kill them tend to “suffer from depression and are haunted by...