Two goals O'Connor had in her stories are as follows: first, God's grace is bigger than whatever horror faces us; and second, God can profoundly touch the lives of very flawed people. In other words, God is everywhere, including with every person who hasn't made the decision to be wholly evil.
O'Connor creates terrible situations in some of her stories. In "A Good Man is Hard to Find," for example, she faces a grandmother with the Misfit, the leader of a murderous gang that has just killed the rest of the grandmother's family. The Misfit is now ready to kill her. This is one of the worst situations a person could be in, but God is there. The grandmother is also an incredibly difficult person, but God touches her life and offers her a moment of transcendence. In her case, because of God's grace, she is able to see the Misfit as her son and reach out to touch him in a moment of pure love before he blows her away.
The reader learns through O'Connor's stories that God is not just there for the holy, the pure, and the good, but for all people in all situations.