Refugee, later today I'll make a character sheet for her so you know her personality and how she acts and reacts. I have not decided what happened to her yet, so hopefully this will help. Heck. Might just start an IC for her.

EDIT: Just read your post. She's not a thief. Smart, strong, compassionate. Willing to fight but never stoop low enough to steal from others. Maybe she broke into your place because she thought it was unoccupied, giving you a scare, hence the current distrust.

Some suggestions:
A. She broke on and took food without knowing someone alive was there. You later realized someone had
 broken in and stolen from you (since you couldn't know it was unintentional).
B. She broke in and you caught her. Scared you a bit, hence the current nervousness, but she was honest and accepted only what you offered her, hence the current kindness.
C. She showed up and you were at the door or on the porch or whatnot. She introduced herself, asked for food, left on good terms. 

Or make something up. Your character, your call. But she isn't dishonest and she doesn't steal. Although she might make am exception for the CoG...