At first an arbiter was a leader of the sangheili forces, but the prophets changed it to a sign of shame, hence why thel vadammee is branded with the mark of shame on the intro cut scene in halo two, because it was his job to protect the halo ring in halo CE and he failed. " you are one of our most treasured instruments, long have you lead your fleet with distinction and purpose, but your inability to protect halo, was a collosol failure." Truths quote to thel. Thel being one of the greatest sangheili fighters and leaders was sent on a suicide mission to redeem his honor instead of wasting his use fullness by simply killing him. Arbiters are meant to die on the battlefield with honor rather than executed, upon being shamed to stretch their usefulness.