When switching to another unit in your squad, the unit/character you had just been using will have it's stance frozen. However, the unit still moves as if nothing else is wrong; it just glides around. This appears to only happen to toggleable stances. Leaning in any direction does not get frozen during a switch.
AI will keep the hitboxes of their stance, but will move as instructed. So, if an AI is prone and frozen in that stance, it can still act, move, and shoot as if on its feet while keeping the prone hitbox. This can lead to exploitation by players to have AI companions who are hard to hit, hard to see, and shoot just as well as an other AI.