The recent Unearthed Arcana Class Feature Variants includes the Bait and Switch fighter maneuver (page 5), which states:
When you’re within 5 feet of an ally on your turn, you can expend one superiority die and switch places with that ally, provided you spend at least 5 feet of movement. This movement doesn’t provoke opportunity attacks […]
The grappled condition states:
The condition also ends if an effect removes the grappled creature from the reach of the grappler or grappling effect, such as when a creature is hurled away by the thunderwave spell.
Assume a monster with a 5-foot reach is grappling an ally; the Fighter is adjacent to the grappled ally, but 10 feet away from the monster. For a picture format, F is the fighter, A the ally, and M the monster:
FAM
What happens if the Fighter tries to use Bait and Switch on the grappled ally?
Best Answer
The grappled ally will be moved, breaking the grapple if that takes them out of the grappler's reach
As written, the manoeuvre doesn't require the ally to be willing, personally able to move or even conscious in order to be the target of the Bait and Switch technique; they merely have to exist and be adjacent to the fighter. Being grappled reduces their speed to 0 but, as is well-established, doesn't prevent any other effects which would move the character around, so the fighter can yoink their ally out of a grapple with impunity.
As @thedarkwanderer points out in this answer, it's already possible for one character to pull another out of a grapple by grapple-dragging them out of the assailant's grasp; this technique is simply a more efficient way to do the same thing. It will likely be ineffective against monsters who are specialised grapplers anyway, as they typically have reaches that are 10 or more feet and so much more than 5' of movement may be required to escape their grasp.