I had a horse who had one leg that would cross under, and she'd trip herself, mostly at the canter. She took small steps at the trot. But the canter was a nightmare because it scared her--and me. She'd be going around, trip herself, and we'd fall down. She'd fall while running in the pasture, too.
I was told to work her in deep sand. I happened to have access to an arena with the deep sand, and it certainly helped.
Also, as I used her to start dressage lessons, it turned out that shoulder-in helped a lot, by bringing the other
leg under, her twisty leg had to take more of an outside thrust. Anyway, she did seem to "outgrow" the falling. To be honest, though, we almost never galloped out, and when we cantered, it was in a fairly collected frame, which helped keep all the legs in place.