A fall is any transitions from airspace (flying) to the ground without landing.
Falls are natural events that can occur without any expenditure of effort. A fall can violate normal rules for traveling between zones.
All falls, regardless of height, produce damage. This damage is considered to be natural shockmancy. This damage may take the forms of injury, Incapacitation or death. All falls represent significant risk.
A city has fallen when all units in the garrison are croaked or captured.
A side falls when the King, Queen or Overlord of a side is croaked, and there is no heir designated. Field units disband, and any cities formerly controlled by the side become neutral.
Neutral cities are frozen and have no turns, only able to react to attacks. Presumably, all upkeep drops to 0, as does all production.