In "A Good Man is Hard to Find," O'Connor illustrates the theme that God's grace can fall on any of us. The grandmother, a manipulative, narrow-minded, difficult person, might be the last person whom we would expect to receive God's grace; but in her moment of need, before the Misfit kills her, she is able to see him through God's eyes. She understands he is like her son and reaches out to him in genuine love, saying,
“Why you’re one of my babies. You’re one of my own children!” She reached out and touched him on the shoulder.
She has every reason to hate this man, who has killed her beloved son, her daughter-in-law, and her grandchildren, but, even though a flawed person, she dies in a state of grace because of the transcendent love she is able to feel for a person who doesn't deserve it.
In "Everything that Rises Must Converge," Julian also experiences the epiphany of sudden love as his mother has a stroke before his eyes. The theme of this story is the transcendent love we can feel for a flawed person. Julian's mother may be a racist who lives with silly delusions about her own superiority, but when she is on the verge of death, all of that burns away and Julian feels nothing but love for her and anguish at the thought of losing her:
“Mother!” he cried. “Darling, sweetheart, wait!” Crumpling, she fell to the pavement. He dashed forward and fell at her side, crying, “Mamma, Mamma!”
The grandmother in "A Good Man is Hard to Find" and the mother in "Everything That Rises Must Converge" are similar in having an innocence and good-heartedness beneath their pretensions, manipulations, silliness, and racism. Regarding Julian's mother, we learn that
She might have been a little girl that he had to take to town....
Likewise, the grandmother has a childlike quality. She is caring enough that she doesn't want to leave her cat behind on the trip, so she sneaks him into the car, and she wants, like Julian's mother, to return to a perceived gentler, kinder past. In both stories, too, adversity unleashes an outpouring of love. What is petty burns away.