According to MLB Rule 7.08d,
Any runner in out when he fails to retouch his base after a fair or foul ball is legally caught before he, or his base, is tagged by a fielder. He shall not be called out for failure to retouch his base after the first following pitch, or any play or attempted play. This is an appeal play.
As far as an example goes, you'll have a hard time finding an one if going by box scores. I'm sure there are examples. Most of the time what will happen is if there are less than 2 outs, the outfielder simply will not run as hard to catch the ball -- or if he is able to arrive to the location of the foul ball with enough time, chances are he will be able to set himself up for a strong throw to the plate. I have to imagine though some outfielders in their earnestness to make an out have forgotten the situation. I've seen situations where outfielders, forgetting the number of outs, have tossed caught fly balls into the stands (a common practice at the end of an inning for a lucky fan) with only 2 outs, allowing base runners to advance -- sometimes scoring a run.