How's the grandmother a misfit in the story? Does she go through a true transformation at the end or is she just pleading for her life?
Critical consensus holds that the grandmother in O'Connor's "A Good Man is Hard to Find" does experience an epiphany before she is shot. She cries out "as if her heart would break" to Bailey, who has just been killed. And O'Connor writes:
His [the Misfit's] voice seemed about to crack and the grandmother's head cleared for an instant. She saw the man's face twisted close to her own as if he were going to cry and she murmured, "Why you're one of my babies. You're one of my own children!" She reached out and touched him on the shoulder.
She sees the Misfit about to cry and understands that he is not so self-assured and certain, that he is one of God's children, too. He is humanized in her eyes.
Ironically, the Misfit recognizes that she does undergo a significant change. He says that she would have been a good woman, if someone would have been there "...to shoot her every minute of her life." Thus, his threat to shoot her brought about a change in her, according to his perceptions.
Of course, the epiphany can be difficult for a reader to accept because the grandmother is so very unlikeable. In this sense, she, too, is a misfit. But that is the point. God's grace, according to O'Connor, is for all.