LSU and our Offense - Burrows

The draft is about the team's exclusive right to offer a contract to a player - not a plyer's rights. A player can refuse to play for the team that drafts him. In that case, the team most likely squats on the rights to sign that player to see if they get a good offer from another team. Are you asking this as if Burrow could say he doesn't want to be drafted so he can sign wherever he wants as a free agent? It doesn't work that way. Even if he takes a year off, the next season he is subject to the same thing.
Bo Jackson is a good example. He refused to sign with Tampa Bay. Owner Hugh Culveyhouse lied to him a told him a plane
ride to Tampa to meet with team officials was not against NCAA rules. It was and cost BO his Sr. season in baseball.

he was re-entered the following year and was drafted by the Raiders in the 7th round.