Discuss the situation with your daughter before you attempt to reach out to this girl. It would be unfair to make your daughter feel that she must be this girl's "savior." Despite the best efforts of your daughter, this girl may have personal problems that are understandably making her a social outcast--problems that need more complex solutions than your daughter could provide. Ask your daughter why she thinks this girl is having social problems and what she thinks could help her. However, your daughter shouldn't be forced to shoulder the responsibility of acquiring acceptance of this girl by their peers. Don't react negatively if your daughter refuses this leadership role. Clearly, your daughter can talk with you and gain advice on how to continue to be kindly to this girl. She may even learn more about empathy and compassion from this experience. Thanks for writing.
Should My Child Play with an "Outcast"?
Toddler and Teenager Expert Advice from Carleton Kendrick, Ed.M., LCSW