The grandmother reveals herself to be a very selfish woman who clings to some kind of religious, outdated moral code and tries to persuade the Misfit that he should do the same. What is notable in this section of the story is how the grandmother does nothing to try and save her son, daughter-in-law and grandchildren. She lets them go off without trying to persaude the Misfit that he shouldn't kill them. She only tries to save herself. Note what she says to the Misfit when she realises she is the last member of the family who is going to be killed:
"Jesus!" the old lady cried. "You've got good blood! I know you wouldn't shoot a lady! I know you come from nice people! Pray! Jesus, you ought not to shoot a lady. I'll give you all the money I've got!"
The grandmother appeals to the Misfit by claiming he has "good blood" as he comes from a good family. She feels that the background you have and whether your family is respectable or not determines whether you are a good person. Her belief that the Misfit is a "good" man leads her to conclude, wrongly, that he will not shoot her. She therefore reveals herself to be selfish, fascinatingly naive about human nature and also she shows that she interprets "good" to mean in alignment with her own moral code and values.
In O'Conner's "A Good Man is Hard to Find," the grandmother speaks to the Misfit about good breeding, Jesus, and seeing good in a murderer during the final moments of her life and the lives of her family. She is characterized through most of the story as selfish because she would rather go to Tennessee than Florida, but she also wants her family to act as well-behaved as she believes herself to be.
As the grandmother speaks with the Misfit in the final moments of her family members' lives, she brings up the two good things in life that she knows about--her faith and her quality upbringing. It is interesting that she doesn't ask the men to spare the lives of her family, but she does ask for her own life because she's a "lady." It's as though the grandmother naively believes that if the Misfit can see that she is a good Christian and a lady of good breeding, then he will magically change his mind and not hurt her.
Another way that the grandmother is characterized is as one who shows faith in humankind even when faced with a serial killer. For example, she appeals to the Misfit's sense of humanity and grace by asking him if he prays. In fact, the grandmother acts like a true proselyting missionary when she says, "If you would pray . . . Jesus would help you." The Misfit agrees that Jesus would help him if he prays, but the problem is that he doesn't want any help.
In the end, right before the Misfit shoots her, the grandmother comes to a realization that she may not have come to unless faced with this desperate moment. She realizes that everyone on earth is linked to each other. For example, the text says that her "head cleared for an instant," and then she says, "Why you're one of my babies. You're one of my own children!" This moment seems to be the turning point in the grandmother's perspective. The Misfit seems to be feeling connected with her like a son feels towards a mother, too. Unfortunately, this is uncomfortable for him, and he shoots her. For the grandmother, however, she experiences a moment of revelation right before she dies. She realizes that even serial killers have mothers and that humanity is all connected. As a result, the grandmother's last feelings are motherly in nature, which means that she may have learned that life isn't about being a lady so much as it is about connecting with others on an authentic level.