I just wanted to throw in my $.02 on an old topic:
I've seen this twice, once in Al Udeid in 2009, and again at Hurlburt in 2014. In Qatar, it was a propeller that came in to the prop shop, and at Hurlburt, I found it on a flameout inspection. In both instances, the bearing in the differential gear in the pump housing failed, allowing the spring tension on the beta shaft to slam to reverse, and in the process snapping off the beta feedback gear. This was different than the case described, however, because both instances resulted in a flameout.