OK Here's the deal with "judicial punishment" (usually it is a heavy cane but whips and even heavy paddles are alternatives)

The client specifically requests it. A majority of Dommes who provide it will NOT agree to do it in a first session. And even after the first session some will try to talk you out of it.

Often it is a very ritualized procedure with the Domme acting like a judge at the beginning. There is either a typed list of offenses that the sub has committed which he has provided or he verbally confesses on the spot. Sometimes the sub actually has done something he feels very guilty about and wants this procedure carried out to wash away his guilt. But then again guys sometimes simply make stuff up with this type of session.

The Domme then pronounces a sentence which she believes is appropriate for the offense "N strokes of the cane/whip/paddle" She then goes from being the judge to being the executioner. The sub is stripped and restrained then gets number of strokes no matter what he says (and with no warm up) Usually it is done very slowly. There is bleeding and marks that take a very long time to disappear

How this got started is rather interesting. In 1994 Michael Fay got a lot of publicity when he received 4 cane strokes in Singapore for vandalism. Afterwards some rich dude located the guy who carried out the punishment and paid him big $$ to come here and do the same thing to him. It soon became a thing with extreme masos.