What happens if the enemy captures your Government Plaza?

[isau]

I could test it to see what happens, but I haven't had a chance. What exactly happens if you lose the city with your government plaza? I assume the plaza is deleted from the city on capture, so the conqueror doesn't get to keep it. But can you build a new plaza after that? Do you have to start over with the buildings? Or are you stuck never being able to enhance government again?