A program that allows Los Angeles cops and firefighters to collect their pensions and salaries simultaneously at the end of their careers was originally hailed as a no-cost way to keep the most experienced officers on the job. But six years into the program it was clear there were serious problems, including reports that aging officers with bad backs and aching knees were joining and then immediately going out on long injury leaves — sometimes for years — at essentially twice the pay. So leaders of the police and fire unions, scrambling to preserve the program in 2008, proposed a seemingly simple solution: require everyone entering to be on active duty.