One answer can be audio books, but that isn't always the answer. Another is working to direct them to that one magic book that opens new doors for them as a reader. One book that has done this for a young reader is Girl, Stolen by April Henry. This is the story of a blind girl who is accidentally kidnapped. It was meant to be a car theft, but the thief did not know that a young girl was sleeping in the back seat. The pace and excitement in this book kept this young reader pushing through to the end. The reader was so excited when they could say that they had finished a YA book.
This one triumph has propelled this young reader to pick up other YA books. They will quite often go back to this same author for new books, but they have also gained the courage to try new YA authors.