Most major forts had a prison section for short-timers but the one I remember being used as a “stick” was Fort Polk. With Polk also being an advanced training site for folks headed for Vietnam the sight of troopies being led through in chains the other direction was overplayed as a sort of object lesson. "Don’t screw up or ---------- "
As for “prisoner run and governed” I very highly doubt it. The closest you may (and that is a big “may”) have had is a platoon or company within a Unit that got the rejects and “company punishment” types. There was rumors about the one company at Bragg being “everyone just short of the stockade” but I cannot confirm it. Either way the Army was under control and woe to anyone who ever forgot that no matter what their rank.