Why does Tom come home after running away in The Adventures of Tom Sawyer?

Tom returns home because he found out their families thought they were dead.

Tom and Joe run away because Tom is feeling sorry for himself because he is worried about Betsy.  He runs into Joe, who is also feeling sorry for himself.

Tom is “gloomy and desperate.”  He feels like nothing is going well in his life.  He can’t see Betsy, and he has been depressed.  Aunt Polly keeps trying natural remedies on him to make him feel better.  He got so upset he gave some to the cat.

When Tom is alone, he runs into Joe.

Tom, wiping his eyes with his sleeve, began to blubber out something about a resolution to escape from hard usage and lack of sympathy at home by roaming abroad into the great world never to return; and ended by hoping that Joe would not forget him. (Ch. 13)

Joe, it turns out, is also running away from home. He got in trouble for drinking cream “which he had never tasted and knew nothing about.”  He assumes that his mother is no longer interested in him.

Huck Finn, Tom and Joe steal a raft and camp out on an island.  Huck basically has no family anyway, and the other two are running away from families they consider unworthy.

Tom sneaks back home and listens through the window.  He realizes that their parents think they are dead.  Joe’s mom and Aunt Polly both feel bad about how they treated their boys.

Tom returns, showing up at his own funeral.

First one and then another pair of eyes followed the minister's, and then almost with one impulse the congregation rose and stared while the three dead boys came marching up the aisle … They had been hid in the unused gallery listening to their own funeral sermon! (Ch. 17)

Tom and the others feel very sheepish.  The town is shocked, but their mothers throw themselves on them, kissing them.  The minister calls it a miracle.  They are forgiven for their transgression, because Aunt Polly and Joe's mother are so happy to see them.