The White Sox move Chris Sale into the closer role due to elbow tenderness:

Sale, who started at Florida Gulf Coast University before making the transition to reliever in 2010, was in his first major league season as a starter. But Ventura said Sale had experienced tenderness and tightness recently, and they felt it was best to return him to the bullpen, where he will close games.

I would think if a valuable pitcher has elbow tenderness, you put him on the disabled list for two weeks to see if he gets better. Why throw him into high leverage situations where he might try to overthrow?