That might be something Burnley consider, but is it something that Ben would consider? It was his big move, but he's become the bridesmaid not the bride. I would suspect he feels let down by Dyche, mis-sold by the used car salesman.
I think he will leave regardless. He wanted to play in the prem, and if not then stay with Boro. Being allowed to play just because Burnley have been relegated wasn't his career path. I doubt another prem team will come in for him now, he will almost certainly want out of Burnley, maybe even if Dyche were to (unlikely) leave.