When cops are fired or forced to resign for malfeasance, chances are they walk straight into another law enforcement job — in LA, the Sheriff's Department operates a revolving door between its police force and its notoriously corrupt jails, transferring its worst police offers into its custodial service.
Indeed, unless a cop is convicted of a felony, it's generally impossible to keep him from getting a job on another force. In some small town forces — like Jonestown, Texas — half the cops on the force have histories of misconduct on other forces. In Florida, there's Crestview Police Major Joseph Floyd, "America's most corrupt cop," who's been booted out of three other forces, for "insubordination, lying, and falsifying records."
Another police officer from elsewhere in the state managed to parlay being fired for drunken driving (and being named in a wrongful death suit that resulted in a $750,000 settlement) into a new position as a sheriff's deputy in another county.
The problem is so pervasive it has its own term: gypsy cops. Moving from agency to agency tends to obscure incriminating paper trails, especially if the switch involves moving from a city agency (police department) to a county agency (sheriff's department) or state agency (state troopers, highway patrol). Changes in background check requirements and decertification stipulations can be abused to keep bad law enforcement officers employed by law enforcement agencies.
The background checks themselves are their own problem. Agencies have been known to hire officers who've failed checks or while background checks were still pending. For smaller agencies or those pressured to add officers, these background checks may not be as thorough — if they're even performed at all.