Ex-barbarians are former barbarians. Barbarians have wild spirits. They tend toward chaotic alignments and they cannot be lawful. A barbarian who becomes lawful loses his ability to rage and cannot train further as a barbarian. He retains all the other benefits of the class (reduced damage, faster movement, able to sense traps, and an uncanny ability to dodge).
Note: An ex-barbarian is not so much a true variant or class, but a penalyzed barbarian (blocked from his ability to rage).