Character Analysis
At this point, you might be flipping back through the story looking for the place where Phoenix's grandson is introduced. No, you didn't miss anything. He is not actually in the story. That is, we only know of this character through other characters' mentions of him. This kind of character is called an unseen character or an absent character.
It might seem weird to do an analysis of this kind of a character. After all, if the grandson isn't actually in the story, how important can he be? Very. The grandson serves as Phoenix's motivation, and the importance of getting to town to get him his medicine drives her entire journey. In other words, no grandson, no story.
So here's the rundown of what we do know about him. First of all, he swallowed lye, a chemical powder used as a household cleaner at the time, which causes burns in the esophagus that can close up the throat so severely that the patient can't swallow well enough to breathe comfortably or eat or drink—nasty stuff.
Second of all, he is waiting for his grandmother at their house, and no mention of any other family member is ever made, so it seems the two only have each other. Like Phoenix, the grandson is strong and determined, with a touch of immortality to him. He doesn't let his pain "put him back at all," and Phoenix is convinced that "He going to last" (91). If Phoenix is a representation of eternal perseverance, her grandson is a representation of the reasons why we persevere—for the sake of loved ones and for the sake of those who suffer and need help.
Additionally, since we assume the grandson shares Phoenix's station in society—namely, poor and black—that he is exclusively dependent on such an old woman with such meager means to his very survival drives home the point that, at the time of this story's writing, to be poor and black was to be primarily left in isolation to struggle to survive.
The Grandson's Timeline