What happens to an AD soldier who fails SFQC, CAQC etc?

Everything you heard is a lie.
JAG has absolutely nothing to do with reenlistment. The terms that go into a reenlistment contract are already authorized and reviewed by legal long before it gets down to the Soldier. Soldier reenlist under option 3 for training, if they fail training they have received the benefit of the reenlistment. No contact can guarantee a Soldier will pass a course.
What happens when they fail is they are released to their old MOS, their branch manager gives them a new assignment and they continue on with their career. Usually they just get moved over to the 82nd since they're already on Bragg

It's not something you are really going to find regulation wise to my knowledge. You are prior service so you are needs of the Army from the word go. You have re-classed coming in, so if you fail that then the Army can roll you back through it, at their option or re-class you entirely, or roll you back to your previous MOS. It's not working a solider out of a contract. It is re-working it based on the soldiers failures. Bear in mind any bonuses are likely lost if tied to a certain MOS.

It's my understanding that the Army will just send you to another location at their needs....whether that be sending you with your old MOS or sending you to school with your old MOS. Your Retention NCO can easily provide good, solid answers to this question.