In Game of Thrones, during the battle of Blackwater, when a lot of fire was spreading from the wildfirea nd King Joffrey seemed to lose the battle, the Hound decided to leave the battle and the city. Before leaving Kingslanding, he went to Sansa and they have the following conversation:
Sandor: I can take you with me. Take you to Winterfell. I'll keep you safe. Do you want to go home?
Sansa: I'll be safe here. Stannis won't hurt me.
Sandor: Look at me. Stannis is a killer. The Lannisters are killers. Your father was a killer. Your brother is a killer. Your sons will be killers someday. The world is built by killers. So you'd better get used to looking at them.
Sansa: You won't hurt me.
Sandor: No, little bird, I won't hurt you.
Why doesn't Sansa leave with him? Sandor has always behaved good with Sansa even in the presence of Joffrey. He even saved her being raped by a mob. For saving her, he was not ordered by anyone, he did it by himself. And there was no motivation for Sansa to stay in King's Landing for both outcomes:
- Joffrey wins: He and Cercei were anyways torturing her. Joffrey was a known sociopath by that time and he hated Sansa.
- Stannis wins: Ilyn Payne would have killed her as Cercei has told him that Stannis cannot get them (Cersei and Sansa). And her brother Robb was enemy of Stannis too, as he has declared himself 'King of the North' and was stealing part of Stannis' kingdom. And anyways, anyone from Stannis' army would not have reaced to save her from Ian Payne.