Base left too soon.

[Illini_Ref]

No out, R1 on first. R1 takes off with the pitch and is not yet to second when the ball in lined to the SS for an out. The throw is back to first to double off R1. The throw goes into DB territory. R1 never gets back to the base. He is awarded third and goes there, touching second on the way. When he gets there the coach tells him to go back and touch first. He does so, touching second on his way back. The defense then appeals. Can the runner do this or not? He was beyond a succeeding base, but NOT WHEN the ball became dead. FED rules here.