Depending on the reason he "failed" the Basic Training (BT) portion of his One Station Unit Training (OSUT). If he was hurt, he'll be repaired and held at his current unit and do odd jobs for the permanent unit members (Cadre) like the Supply Sgt or 1st Sgt. Once whole and able to perform, he'd be "recycled" into a unit that is the same training module as he was when he got hurt and life goes on.
If he can't be repaired and made whole, he'd be discharged but honorably and possibly with a disability payment. It can get complicated here and often times a lawyer may be needed to fight for him.
Now, if he just can't meet the standards of a portion of BT (Can't do enough push ups, lousy at shooting a weapon) or what ever training he's in (I'm assuming he's in BT as it's the first course and none progress without completing it) then they'll give him extra training to try to get him through or again, recycled into another unit to try again. Ranger, Airborne and other advanced courses work much the same way. The Army spends a boat load to recruit these people and don't quit on them easily so normally there's ample chances to succeed.
In my 5 years at a BT and later a OSUT company, I saw many injured soldiers convalesce, recycle and then finish their BT and move on. I saw a small hand full medical discharge out. I also saw a lot of them just plain quit. Yes, it can be done but the Army doesn't just let you go and it's not simple but it does happen. There's not enough info here to know what's going on with this particular soldier but it sounds to me like he doesn't want to recycle or he found out how hard Army life can be (And he's in the BASIC portion, it gets MUCH harder) and prefers life at the Piggly Wiggly. No shame in that, it happens all the time.
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