Final Fantasy VI, actually; you’re probably thinking of the Rippler bug. To provide some extra context not delved into by the linked article:

• Final Fantasy VI’s game engine doesn’t distinguish between being immune to a given status and permanently having a given status; it just has a single “status lock” flag which, when set, makes it impossible to gain the status in question if you don’t already have it, and impossible to lose the status in question if you do.
  
• Most things that alter a character’s behaviour or available commands are implemented as statuses in Final Fantasy VI, sometimes in conjunction with the status lock flag. For example, the “Counter” status (which makes the affected character perform a melee counterattack after being struck) normally goes away after it procs once, but the Black Belt accessory both inflicts the Counter status and sets its status lock flag, preventing it from “curing” itself.
  
• There’s an enemy ability called “Rippler” (also learnable by Strago as a Blue Magic/Lore spell) which causes the user and the target to exchange statuses. It ignores the status lock flag when doing so; this is intentional, because Rippler is meant to be able to do stupid tricks like poisoning a character who’s immune to poison by poisoning yourself and trading statuses with them.
  
• The actual bug is that it doesn’t check whether the targeted status is something that it makes sense to be able to transfer between characters, presumably because whoever programmed it forgot that being immune to a status and permanently having a status aren’t separate states in this game, and thus didn’t realise that making Rippler ignore status immunity would also allow it to steal existing statuses that were meant to be immutable.
  
• The upshot is that Rippler can steal statuses like “riding in Magitek armour”, “being at critical HP”, or even “being absent from the battlefield”. (Though it takes some finagling to target a character who has that last status in the first place!)
  
• Most of the time this isn’t a big deal; the “being at critical HP” status automatically reapplies itself at the start of the next battle if you meet its criteria, for example, and the “being in Magitek armour” status is event-exclusive anyway. However, Shadow’s dog Interceptor, who can defend and counterattack for his master in battle, is implemented as a modified and status-locked version of the Counter status (see above), so Rippler’s status-lock-ignoring behaviour effectively allows it to steal your dog.
  
• What’s worse, the Interceptor status is normally only applied or removed during story events when Shadow joins your party; nothing else is intended to be able to modify it, so the game doesn’t ever check whether Shadow has the Interceptor status when he shouldn’t, or lack it when he should – it’s simply assumed that this can’t ever happen.
  
• This means if a monster uses Rippler to steal Shadow’s statuses after his last possible recruitment event, and the battle ends without getting them back, the Interceptor status is permanently gone – that monster not only stole your dog, it ran off with it!
  
• The monster that can use Rippler which is most likely to be encountered during times when Shadow is an available party member just happens to be a really big frog.
  
• Thus, a frog can steal your dog.