There is a plotline involving this in the first season of The Line of Duty.

It opens with a guy who's complaining to the police about the frequent robbery of his house. They view him as a nuisance and try to respond to his complaints as little as possible.

Eventually someone is apprehended committing a different crime in a different location. An officer visits him in the hospital (there was a mighty struggle before he was caught) and asks if he'd be willing to lower his sentence by potentially resolving some other outstanding crimes that the police are investigating.

She reads off a list of crimes, and he responds "yeah, that was me" to everything she says. One of the items is the several robberies of the guy we met earlier.

It's win-win; his sentence is lowered for doing the police a favor, and the police report a higher solve rate.

After that, the original guy who was always brushed off suffers another robbery. Since he happens to be home at the time of the latest one, he is severely beaten.