(The following situation probably isn't that common. I just tried a little experiment and - as always - discovered a probable bug.)

A crystal crag is within the borders of a city (Lakarra): screenshot https://www.dropbox.com/s/a6jy0gr9doeai96/2013-01-07_00001.jpg, savegame https://www.dropbox.com/s/8wgqqtmpgm6nwk5/before_raze.EleSav.

I raze the city; the crystal crag loses its improvement but keeps its own zone of control around it: screenshot https://www.dropbox.com/s/es2s6jcgln4ua9z/2013-01-07_00002.jpg, savegame https://www.dropbox.com/s/qa9pr6fh6sgtw24/after_raze.EleSav.

At the start of the next turn, the resource is still within my zone of control, and I get the offer to build a (new) improvement there: screenshot https://www.dropbox.com/s/i6cqjlot7sk0j6c/2013-01-07_00003.jpg, savegame https://www.dropbox.com/s/9tsznom1gehgfue/next_turn.EleSav.