Punishment and shame are intrinsically linked.

Punishment comes to enforce shame when shame is not naturally incurred in whoever committed the shameful act. Or, punishment can compound a shame that is already felt. Sadists fetishize shame, which is why they love masks.

There is only one historically verified record of a public sighting of the Man in the Iron Mask, who really existed. His jailor paraded him around the town square, for no apparent reason. The behaviour was odd, considering the masked prisoner was in his predicament for the exact reason that he must not be identified by the public. Then why parade him? To maybe increase his shame.