That's what the Giants did, essentially sending the message to other players that if they don't take a lowball offer, an arbitration win will be pyrrhic:
“I can’t speak for everybody, but I know there’s a lot of blowback,” he said. “There was definitely some concern amongst some (pre-arbitration and arbitration eligible) players, like, ‘What if this happens to me?’ If one team does this after going to arbitration then it turns into 70% of teams, what’s to stop teams from just making the lowest possible offer knowing no one will take them to arbitration? That bothers me for future players in this situation.”