In a situation where B1 does not swing and F2 catches the pitch then drops it, what is B1 allowed to do?

In this scenario, B1 is allowed to leave the batter's box once the pitch is thrown and caught, even though they did not swing. The act of catching the pitch and subsequently dropping it does not impose any restrictions on B1's movement. Since the pitch is considered a standard delivery, B1 is not bound to remain in the batter's box under these circumstances.

B1 can indeed leave the batter's box and has the opportunity to advance to first base if they choose, as the ball is considered live once it is caught, regardless of whether it is a strike or ball. The key point here is that B1 is not penalized for not swinging at the pitch and can assess the situation after it has been caught and dropped by F2.

The other choices imply restrictions or automatic outcomes that do not apply in this situation, hence they do not accurately reflect the rules governing a dropped ball by the catcher following a pitch that is not swung at by the batter.