What is the longest you have heard of someone lingering around in Basic training?

Friend was in BT for 1 year fainted at graduation and dishonorable discharged

As a Basic Training Company Commander at FLW in about 1990 I had one guy who was held over because he was slotted for language school and they got incredibly delayed in getting his background investigation for Top secret done. If I recall correctly his family was way out in the middle of Montana and the nearest FBI office was 150miles away so getting in person interviews were hard to do. We ended up running through on of the Engineer AITs just to keep him usefully busy. I think that was about 13 weeks after graduating from BT.

We had a dude at Fort L. Wood that got recycled for multiple reasons, multiple times. The last time he got recycled he hurt his hip. Finally got there and went to his unit with 1 month to clear and ETS

I went thru Basic and AIT at Ft. Sill from Jan-Apr 1984. We had a soldier that was a recycle that completed his training with our platoon. He said we were his 3rd recycle. He had broken his ankle on the obstacle course on the first cycle and failed some of the common tasks on the second cycle. They were going to send him home but he asked for one more shot and they gave it to him and he made it. I admired his willingness not to quit. I don't know what happened to him after basic but at least he completed it.

I knew of a guy during Covid who was at Benning 2 months before ever starting. Someone would show up with Covid so the whole class would have to quarantine for 14 days. He finally got to start and finish after 2 months.

I was sent to Ft. Sill in 1989 for 13B AIT (as an E6) and there was a private there that had graduated 6 months earlier but was held over because they didn't have size 18 boots for him. He did BT in running shoes and then was assigned to HHB as a gofer until someone made him some boots. He had to duck when he went through doorways. BIG guy!

I had basic at Ft Leonard Wood in '66 and had this little guy with huge glasses trying not to 'boolow' for the THIRD TIME... He made it with us due to the 'fudging' by the DIs on his PT and weapons fire scores. I was told that if someone recycled (boolowed) the DIs did NOT get extra time off between cycles. I went on to AIT at Leonard Wood and the kid went on to some infantry outfit for his AIT. I still have my Yearbook and could find him there, but what's the point.

I was a Marine, there was a guy who spent 2.5 years in boot camp, back in the 1960'w

When going to basic, I saw a guy who claimed to have been there three times. I often thought he was a plant, the cadre put there to spy on recruits. He had a good story, but in the end, I thought he was full of it. Sure enough the day before we went to our assigned basic unit, he got "pulled" again.

When stationed at Ft Leonard Wood, September 2000, I was processing through and was assigned to a reception batallion and treated as Cadre, because we were all prior service. Part of our area of responsibility was taking care of the Hold-Under barracks (those waiting to goto basic training). The Drill Sargent told us, some of them had been there for over a year, waiting to start basic training. That's how backlogged they were. That doesn't cover those who failed initial PT, or had medical or legal issues.
They even had a couple of recruits awaiting court martial, before they had even started basic. Clack Marketing, and destruction of government property. Of course, they could have got off with an Article 15 (non judicial punishment), but the barracks lawyers talked them into holding out for the court martial. I am sure they lost in the end.

After 8 weeks of boot camp, we got on the busses to leave for the airport when one of the guys flipped off the company commander as the bus was leaving. Company Commander made the bus stop, got on and grabbed the guy by the lapels on his pea coat and dragged him off. Met up with the guy about 10 weeks later at school. Company commander hauled him directly to the XO where he was given the chance to start over - on the first day of boot camp.