You are describing the Browns. When they had nothing at QB, they constantly tried to find their QBs later in the draft. Quinn, Weeden, and Manziel were late first rounders. Kizer was a second rounder. Frye, McCoy, and Kessler were third rounders.
Over and over, the Browns had super high picks and the easy ability to move up higher to get one of the top QBs, but what constantly happened was a new regime would be taking over, would declare the cupboard to be empty, and would say they need to trade down to get more assets while taking a QB late saying they really like that guy and, you know, Brady was a 6th rounder. It was a loser attitude by idiot GMs who were afraid to attach themselves to a highly drafted QB out of fear they'd be fired if that QB didn't work out, yet all of them ended up fired largely because their bargain bin QB choices resulted in dead last division finishes year after year.
