Here in Tolley's video in the Texas state crit champs, the breakaway laps the field. Then Matrix lapped riders in the field go to the front and drive the race (one of their guys was in the break), and split the field. Tolley questions whether this is allowed.
It clearly is allowed by the rules. The only restriction is that you can't fall off the back of the field and help a break. Yet there seems to be mass confusion among riders about this issue still. And also a feeling like even if it's allowed by the rules, teams should not do this. The break has to decide whether to lap the field or not. They don't necessarily have to. And if they don't, then there won't be any break/field chaos.