In Game of Thrones, during the battle of Blackwater, when a lot of fire was spreading from the wildfire and King Joffrey seemed to lose the battle, the Hound decided to leave the battle and the city. Before leaving King's landing, 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 well with Sansa even in the presence of Joffrey. He even saved her being raped by a mob. He was not ordered by anyone to save her; 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 Cersei were torturing her anyways. Joffrey was a known sociopath by that time and he hated Sansa.
- Stannis wins: Ilyn Payne would have killed her as Cersei has told him that Stannis cannot get them (Cersei and Sansa). And her brother Rob was enemy of Stannis too, as he declared himself 'King of the North' and was stealing part of Stannis' kingdom. And anyways, anyone from Stannis' army would not have raced to save her from Ilyn Payne.