The Yoren's task says :

Any phase : Discard 1 night's watch character from play to search you deck for 1 different night's watch character, reveal it, and add it to your hand. Then shuffle your deck.

If I save the night's watch from being discard, I can always search for an other night's watch, or the cost of the event is considered not paid?

Mitch1974 said:

The cost is considered not paid so you can't search (and you waste the event). When an effect says do X to do Y, "do X" is considered paying a cost (and paying the cost must be done in order for the effect to resolve).