Troublesome police officers can sometimes keep their jobs or get new ones in the U.S. To find out how it happens—and how frequently—The Wall Street Journal for an enterprise article tracked the whereabouts of officers involved in incidents that made local headlines and caused them to lose their jobs, receive a criminal conviction, or both.

At least 10,000 arrests of law-enforcement officers between 2005 and 2011 made news reports. There were thousands of separate citizen lawsuits filed against officers during the period. Law-enforcement...