When I'm behind in culture, the usual result of a despotic rush with a non-religious civilization, I go even farther and never garrison with units that I would be concerned about losing. I park enough units right outside the city to retake it when it flips. Then, once I have wiped out every last city of that civilization, I move lots of units in and quickly quell the resistance in all their former cities.
Usually these captured cities can become useful only after you can get a great leader and build the forbidden palace in one of them; so it costs little to leave them in resistance.
When I'm fighting a war against someone that I cannot expect to destroy soon and I capture a city with a Wonder in it, I use conscripts as a garrison.
I have not figured out what happens to the units that disappear from a city that flips. They don't seem to go over to the enemy. Do they just vanish?
The most annoying case is a once-great civilization that survives only in a single city on a distant island. I've lost big armies in cities that "admire" the past cultural glories of such civs.
Before the patch it was proposed to keep an almost-conquered civ around as a vassal state. Since the patch I think that is a terrible idea.