In some novels, the hostages themselves may find a way to escape or overpower their captors. This could be through a collective effort or the discovery of a weakness in the captors' security. For example, in a prison - break - type scenario where the prisoners are the 'hostages' of the prison system. And in other cases, it could be a negotiation that results in the release of the hostages, where the captors' demands are met in some way, but not always as they expected.
Well, in certain fictional novels, there could be a deus ex machina - like solution. Maybe an unexpected event or character shows up that changes the whole situation. But in more well - crafted novels, the resolution of a hostage situation is usually tied to the development of the characters and the themes of the story. It could be about redemption for the captors, or the growth of the hero as they face this difficult situation. The resolution is often a culmination of the build - up of tension and the exploration of the relationships within the hostage - captor - rescuer triangle.