My suggestion is this: cops can turn on/off their duties, as a strategy for catching thieves. When the cop is in off duty status he can't do cop jobs and he's not marked in blue on the map - so he can approach the thieves without the look of thief. Then, he turn on duty and can fine/arrest again.
We can have a limit of time to change the status, like 5~10 minutes...
We can have a limit of time to change the status, like 5~10 minutes...