I am not a lawyer. That being said, I believe a person convited of a crime must report it to the SSA immediately. People who are convicted of a crime generally do not qualify for SSD benefits, as stated in this link:
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I would assume that you're writing this from Michigan, correct? Going on what I know about the HYTA, as long a person completes the program they should not have a criminal record and therefore SSD benefits should not stop. That being said, I do not know how this affects a young person assigned to finish an HYTA program. I would assume that if the offender fails to complete the HYTA program without incident, their conviction may stand on their record and possibly prevent them from getting SSD benefits. Since the criminal record of someone sentenced under the HYTA is nonpublic, your friend's SSD benefits may be safe.
Hopefully this online pamphlet provided by the SSA helps in a little more detail: (removed)
This is definitely something to speak to a lawyer in your area about.