Anything face-saving protects you from humiliation. Slip and fall in the school cafeteria, and you might use the face-saving tactic of pretending you did it on purpose. You know, for a joke.
The concept of something being face-saving varies between cultures; what's undignified or dishonorable in one might be no big deal in another. It's all about the idea of face, or dignity in front of a social group, and the potential loss of it. In a negotiation between two countries, the winning side sometimes grants some face-saving concessions to the loser, to make their loss less humiliating or embarrassing.