Not aware of any tourneys with this tweak, but I use a similar example when I teach.

If the payoff from exiting is zero and the mutual defection payoff is negative, then the game doesn't change much. Exit on the first round becomes the unique subgame-perfect equilibrium of any finite repetition, and with a random end date, trigger strategies to support cooperation work similarly to the original game.

Life is a more interesting if the mutual defection payoff is sufficiently better than exit. Cooperation can happen in equilibrium even when the end date is known (except on the last round) since exit is a viable threat to punish defection.