Gosh I wish we'd see that sort of collective action.

In 1994 during the Caribbean cup, Barbados was playing Grenada and needed to win by 2 goals in order to advance. They gave up a goal late making the score 2-1. They had a golden goal rule at the time where any goals scored in extra time counted as two. Barbados scores an own goal to tie it and push for extra time. Grenada was in a position that if they score in either net it's a benefit to them, so Barbados had to defend both goals until the end of regulation.

It's not quite like playing to lose, but it's pretty close and super entertaining.