Yes, they do. My daughter rode one that was domesticated about 3 weeks ago. It was caught by an old Apache named "Yellowhand" and it took the guy 3-4 days to finally catch him. The Federal government brought him in after they couldn't get close to the mustang after a few weeks of trying.
But yes, they round them up and sell them at auction or directly to local ranches that are interested.
Seems we need more Apaches...
appreciate that info