Civilization – Why can’t I enter a city-state’s territory

If you kill quite a number of units of a city state and/or keep trespassing on their territory enough to get your score very very low over an extended period of time, they eventually will be convinced that you are so evil it's not worth considering peaceful coexistence, so they will be in perpetual war with you. You will not be able to buy their friendship and relations will not heal by themselves over time.

Actually that doesn't mean too much, though. If you go near them, they'll attack you, and if you leave cities undefended near them, they'll capture those. Apart from that, they won't hunt you across the map and they won't make others hate you as well. If you just leave them alone now and make their area taboo to your units you can still get along with the other city states just fine.

You might choose to have one perpetual warring city-state next to your army outfitter because city-state units train your troops longer than barbarians do.

So based on Fabian's answer here combined with Oak's experience mentioned in the comments for this question, it sounds like razing a city will cause all tiles that were acquired by that city to become neutral, as well as all tiles in the immediate ring around that city, even if those tiles were not initially acquired by the city being razed (beacuse as Fabian pointed out, building/capturing a city will automatically transfer ownership of tiles in that inner ring that belong to other cities of the same player to the "new" city). Any tiles in the inner ring that do not belong to the player owning the city should not become neutral.

Unfortunately, I am not aware of any way to determine ahead of time which city initially acquired a tile and thus "owns" it for purposes such as this.