They don't fall off the edge! They're gasses! They gather there, that's why the edges are so foggy. It's all the gasses built up. Then, when they turn on "the Sun" for the day, the gasses reflect all the heat back across the disc.

When enough build up, they have boats with huge leaf blowers on them. They blow all the gasses around, and make "clouds" to hide what they're really doing up there.

(This is roughly based off the ramblings of a co-worker I had. He was the first Flat Earther I ever met in person. Good worker, wish Flat Earth was the dumbest of his beliefs.)