Barl's Cage

• WWizards of the Coast2004-10-04
  Official Ruling
  Does not prevent a creature from untapping at other times. It just stops the “normal” untap during the untap step.
• WWizards of the Coast2009-10-01
  Official Ruling
  You may target any creature with this ability. It doesn’t have to be tapped.
• WWizards of the Coast2009-10-01
  Official Ruling
  Barl’s Cage doesn’t track the creature’s controller. If the affected creature changes controllers before its old controller’s next untap step, this ability will prevent it from being untapped during its new controller’s next untap step.
• WWizards of the Coast2009-10-01
  Official Ruling
  If the targeted creature is untapped at the time its controller’s next untap step begins, this ability has no effect. It won’t apply at some later time when the targeted creature is tapped.

Rulings via Scryfall