I've only encountered this exact nonsense in Fallout 4, but it's nonsense worth addressing.
In that game, you can tell your companions to equip nearly anything you can equip, and any bits of armor they equip will take up an armor slot (such as left leg, right arm, torso, etc).
Their default outfits tend to take up their arm, leg, and torso slots, so if they're wearing their default outfit and you tell them to equip something on their left arm, that's suddenly all they're wearing (aside from headgear). They won't automatically put the default outfit back on if you take the left arm gear back, either.
What's also funny is that said left arm gear could easily provide more protection on its own than the default outfits.
This doesn't happen in any other games I've played, though it wouldn't surprise me it there were games I haven't played in which similar could happen.