The rules state:
(Generally, it does not make sense to
attempt passage of the Law if you do not have sufficient
Influence in the House.
I think I may have found an exception. Suppose you would like to discard a Law card but there is an Any Law could which you want to retain. Any Law cards are valuable in the Events display because they bring in 6 PW and keep the Opponent guessing as to what to block. (Okay, okay - this is mostly a Justice tactic.)
So you pay the cost of the Law card you do want to discard knowing it will fail. As it failed the opponent does not get any PW. As a bonus this was not a Last Action so you are free to play an Organization/Violence card.