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Continuity mistake: When Billy finally finds his mom and talks to her in front of her apartment, the door behind her changes from (almost) fully closed to much more open, to an intermediate state, and fully closed again at the end. (01:25:30 - 01:28:00)
Answer: He went out of his way to protect his new foster brother, who's disabled mind you, when he was being picked on by the Steven King novel bullies. He showed he had some virtue. And, on top of that, his other behavior, like stealing the police car, while bad, did have a noble reason behind it of him trying to find his mother. So he wasn't perfect, but he had some virtue. And, as the old wizard said, he was out of time and Billy was his last choice.
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