Somebody explain how a coaching change contractually works?

Seems crazy that Lsu would put themselves in position to rely enough on a verbal agreement with sexton to let Miles go, and then leave themselves hanging in the breeze while sexton shops fsu or other schools for a counter offer. But possibly that's what's happened here.
My question is can they sign the new coach to a contract that spells out pending the release of current coach? (Before releasing the current coach) . Then it becomes official once the current coach is let go? (Kind of like buying a new house, pending the sale of your current house, so you don't get screwed into owning 2 houses when your sale falls through).