This unnamed woman was the wife of Cole Trenton.
One morning during breakfast, Cole got a fax with a picture of Dean Winchester and the word "yup" on it. Even though she didn't see the fax, Cole's wife guessed what it was about and asked if it was "him." Cole's silence was enough of an answer for his wife who walked away, visibly upset.
During the confrontation between Cole and the Winchesters, Sam reminds Cole of his family, having overheard Cole's conversation with them. Sam suggests that Cole's wife and son need him to return and to return whole. Having learned the truth about his father's death, Cole gives up his vengeance and returns home to his wife and son.