The Moment. The moment of moments. He gave her his cloak, to protect both her dignity and ensure the end of her torment. When a man gives a woman his cloak, he promises to protect her as long as they both are living. He later offers to fulfill the promise but she refuses in fear so he instead rescues and protects her sister. The last two accounted for Starks are still alive because of the promise he makes to this girl. Even if he never said it out loud.