I've often wondered who started the notion of putting a curb strap on a snaffle. You won't find one in the UK or Europe, just here in NA. If the rider is pulling one rein so hard the bit slides thro the horse's mouth, it's time to rethink the training. The curb strap is ineffective in preventing the bit from sliding thro because the strap is so loose it will just go thro as well. So will part of the headstall. The size of the bit rings is what helps prevent the bit from sliding through and the horse's mouth would have to be gaping open.