Can delinquent credit card affect other family memeber not on account?

Got approved for credit card, when I did application (not jointly), but by myself, at the end of application it asked if you would like a second card for a family member to use from same account. I put my daughters name down since she was in high school, and sometimes needed money when she was out with friends. Keep in mind this was a single account, not joint. Well I could not keep up with payments, and the collectors call here asking for me and my daughter. I dont even think I had to use her SS# when I used her as the other family member for the second card. I only think I had to use her name. How could they put this on her, How could this affect her credit if it was MY account???? They call and ask for me and my daughter, shouldnt they only be asking for me?????