With Black Death in-play, the game only ends once there are no deaths for two phases. To achieve this Black Death must be eliminated through banishment.
At the start of the game, a player is chosen to be the first victim of Black Death. They may be chosen randomly, by the Hosts, or by a spectator/similar. That player will die at the end of the first night. When the next night begins, they must choose the next victim of Black Death. This is a forced action, but they are unaware of what their action does. The only way to stop this chain of death is to banish the player who would receive black death next during the day.