When a city falls into the hands of an enemy side, the conquering side can choose to sack the city, reducing it below level 1 so that it no longer functions as a city. The resulting site is similar to ruins and can randomly pop Barbarian units, gems, and Magic Items. The city site may be claimed by any side and rebuilt.
Sacking may be a form of Natural Dirtamancy available only to Rulers, and implementable by Warlords they authorize to use it.
The side doing the sacking gains an immediate increase in their treasury.
Kona, a Level 3 city, yielded 20,000 shmuckers when Faq sacked it, while Progrock gave 40,000. This would seem to indicate that each level of a city doubles the gain from sacking, unless there are modifiers that haven't been mentioned yet.
A Side can sack it's own Cities if the need arises.