I don't know. Can someone else help?"Some" buildings? Randomly? Or pre-determined, which might be why you chose to mention cathedrals? So are a number of buildings pre-determined? Do all of the go away?
I think all buildings that add some culture will disappear, all WW will stay and granaries and the like have a chance of disappearing if it is not a city-recovering.
The thing is that there is a bar showing nationality in the city screen. I assume it is there for a reason. I just don't know what that reason is. Do you?
Maybe to make you know why they don't want to fight that country? Or to show you the flip probabilities? It is just information.