Nothing really juicy, but I remember seeing offers of a couple of hundred quid (the exact figure escapes me now) to be offloaded from LHR-MIA and similar flights from time to time, to fly the next day. Like PAXboy, inevitably this always happens only on occasions when you have to get there exactly when you're booked to.
I have much more often claimed the benefit of this sort of "helping out" by offering to go on an earlier flight that I've arrived in time for. If they need help, they'll happily move you to an earlier flight even on the cheapest non-changeable discount economy fares. But then it may be that my FF account has the notation "too expensive to allow him to hang around in our lounges" in it.