It was recently done in the independent Frontier League, under their sudden death tiebreaker rule.
If a game is tied after 9 innings, they play a 10th inning under the free runner rule. If still tied after 10, the tiebreaker rule is invoked. Works like this:
The home team decides whether they want to go on offense or defense. The team on offense places a free runner on first (not second) and they play a half inning as normal. If the team on offense scores, game over, they win. If they don't score, game over, they lose.
So if the game is scoreless after 10, a team can win (and has won) without scoring a run.
Obviously the purpose of the rule is to get games over with. It is not uncommon for MLB to use the Indy leagues as a lab to test proposed rule changes. I don't see this one going anywhere though.