The thing about this is that fights between crims and cops are usually fast paced, and usually happen like this: cop and crim see each other; cop and crim fight; one dies; the end. There is very rarely a proper stand-off like we would expect to see.
Maybe, when taken down by a police officer, criminals re-spawn at the police station, and are put on a sort of parole.
When on this parole, if the criminal commits a crime, no matter how small, their wanted level is automatically set to 30 and they are marked on police/SA army mini-maps. If the criminal is killed/arrested while on this parole then they are sent to prison for 200 seconds.