These are called Second Chances - from the Update Notes
Introducing Second Chances Have you ever battled your way through a tough dungeon, only to be disappointed that you didn't receive the reward for your School? Well now players can pay a small fee to get a second chance at what's in the creatures pockets!
Many final boss encounters will contain a chest in the room that offers players a second chance to get the item they wanted off the creature they just defeated. Simply use the chest after your initial duel, pay a few Crowns and you are given a second chance at the exact same rewards the boss drops normally. These chests can only be used a certain number of times per day per character.