Presumably it's produced at the same rate but destroyed by drying out and cracking as it gets longer and has less access to oil, so it slows down and may find an equilibrium where it stays the same length.
Sure. If your hair is breaking off at the same rate it’s growing it’ll be a stable length. I have no idea if that happens though. It seems farfetched that hair would actually be splitting that’s aggressively unless it’s visibly very unhealthy.
If you take proper care of it (which includes trimming split ends so that the cracks don't propagate) then sure, but I've previously neglected my hair to the point where my split ends had split ends. I'll absolutely cop to "visibly unhealthy" but there does come a point where the ends start to fall apart and break off easily.
But I am also pretty confident that hair does not stop growing because of split ends. That feels like an “old wives tail”.