Dear r/Law, I have a question for the hive mind about the law of civil penalties.

When are civil penalties paid to the State (or Federal) Treasury, and when are they paid to the plaintiff in a suit?

I've tried to look this up and all I've found is a reference to (at least in some) State judges being optionally able to direct civil penalties for contempt to a party if that party is being harmed by the ongoing contempt, as a sort of redress. Do you know of any other situations where civil penalties are paid to a party to a suit, rather than the Treasury?