Rich and poor
Police is not here to protect every person from violence, it is here to enforce law. (Already ruled and practiced in our world.) In the future there is big difference between those rich and those poor.
There are hight-tech citites (or enclaves), where the rich lives, protected by police and without the need to violently resist (as they could lose their status). The police is benevolent, as usual crimes are white collar crimes (tax evasion and such - solved by penalties) and ocassional interpersonal violence in affect (cheated husband would broke nose his wife and her amant when catch them in flagranti - and then give himself to police without fight - and get away with huge sum to fix cosmetical damage and emocional hurting, maybe even few weeks or month in nice prison - nothing to risk life for). And the police is benevolent, as there is no serious resitance and we are talking rich peoples. In city is total surveliance, cameras everywhere, credit cards with names on them only accepted and so on - nearly impossible to run away from police for more than few hours anyway in bounds of such city.
The cities have good guarded borders and crossing the borders (both ways) is generally frowed upon and is matter of checks like taking intercontinetal airplane today.
Outside are "slums" with poor people, left to themself. No state cameras would stand long there, risky for police to go there without big group and military equipement. Law there is more encorced by customs. Cash is used regularry, IDs are not mandatory to live there and violence is part of the life (also vendetta, low mob mafia, and such).
Well some people are very rich there too, as well as in the city are not-so rich people (gardeners, maids, basically all services) - but those in cities are controlled and wants to keep their good status, those in slums wants to keep their independence and privacy (or are forced to). (basically average person in "slums" can own more, than the lower class in city, except the safe environment and guaranteed good life, including medical care)
There is possible migration both ways, but it is difficult to change status:
poor to rich means give all your privacy, be penalized on all proven crimes and be subject of long time suppresion of police as unttusted person - also you need somebody rich to promise overlook over you (and pay all eventual fines for you) and you would go to the bottom positions anyway and basically be slave for years before having chance to get better position, while your patron can send you back to slums on his/her whim (so you would lose everything in both words)
rich to poor - well, if you think you can survive in jungle, where nobody helps you and everybody hates you, without all those nice thinks you had in city guarantied - you need to be really desperate to go this way - and the city would not like to accept you back. Also all your relatives would lose a lot of credibility aand status for your action, even if they disown you - do not count on some support.
Anyway the cities needs the slums for taking care about agriculture, mining, low tech (which does polution), artworks and such, while slums need cities for high technology, medicines, movies, etc. so there are big trade routes both ways.
And those bounty hunters operates outside the cities, both for locals and citizens, who had problems outside city walls. Maybe even some bounty hunters have homes in cities and high technology (private SWAT), but the main body lives in slums and knows the back streets, gangs and all others, who operate there.
Bounty hunters are not allowed to operate in cities (the police can manage it there good enought), but police cannot operate in slums (as nobody cooperate there and small units would be attacked for equip and ransom, while big units have no chance infiltrate anything), where bounty hunters can move freely as locals. There is tell-telling difference between citizenc and locals not only in body modifications and equipement, but mainly in behavior, street knowledge, language ... they both just stand out on the other side of border.
Referencies: District 9, Battle Angel Alita, Demolition man, Ghost in the Shell, Black Lagoon, ... (or with some exgregation rich countries (as "cities") vs poor countries (as "slums") today)
Edit: It is just on you, what "poor" means in that setting - if common food is soya-ratburgers as real meat (even from vermints) is too expensive, or if it means, that some of them have "just" 2D TV without tactile feedback, only a two or three pieces of cyberware enhancements and have to travel by ground vehicles ... poor and rich is just relative to each other.