The 747 classic has a backup control using separate electric drives for the inboard and outboard trailing edge flaps, but it is rarely taught to the pilots and most do not know how to use it. After the Japan accident Boeing offered a fuse for the #4 system but many operators did not do the mod because it costs 110k or so per airplane.
The 744 has the fuse, so it should not suffer the same complete failure. Dunno about the 777.