In The Road, the boy and his father have been struggling to make their way to the coast and to find something better than the existence they have now. Recently, they came upon a refuge and were able to sleep and shelter and replenish food stuffs, after having been starving for days. They leave refreshed - relatively speaking- the man having been "ready to die and now he wasn't going to." Unfortunately, they can't stay too long for fear of being discovered.
Having moved on, they come across an old man who "even by their new world standards," smells terrible. They are wary of him and he of them but the boy persuades him to eat something. His father knows that teh boy will want "to keep him" but it is not practical. It is only the boy's insistence that the man even gives him food and waits till morning to continue on.
The boy's father tries to tell the man that he cannot go with them. He knows and he suggests that he predicted something like this catastrophe would happen but people just ignore the signs: "tomorrow wasn't getting ready for them. It didn't even know they were there."
When they are ready to leave the old man and the boy's father discuss how terrible it would be to be the last person alive,even if accompanied by a god because "to be on the road with the last god would be a terrible thing so I hope it's not true. Things will be better when everybody's gone."
It will even be the end of "Death." The old man says "Death" will wonder "where did everybody go?" He feels relieved that it will be that way.