How does that work? I.e. say a kidnapping occurs and the ransom is paid. What kind of trouble does the paying party get into? A fine? Jail?

So long as the potential payer knows they will get something they are going to slow down. They might pay, but suddenly becomes harder because they have to hide what they are doing. Many won't figure out how to pay.

The real value though is enough people consider themselves honest and won't do anything they know is illegal. They already hate dealing with criminals, but so long as paying is legal they might do it, but as soon as it affects their moral code they won't. The whole system collapses because just a few people saying no to paying means the kidnappers lose money on too many operations.

I understand the mechanism and the point of making it illegal, that’s not the question.

What I want to know is what exactly are the lawful repercussions for the person who paid.

A fine or sentence is probably on the books but it never comes to that. The main thing is to freeze the family's assets, and more importantly to publicize this procedure so the mafia or whoever knows there's no point in threatening the family.