The sheriff is an unnamed character featured in the Bounty of Blood DLC.
Background
The unnamed sheriff has been living in Vestige for few decades, although it is unclear when did he take the responsibility of sheriff on his shoulder. He is respected among Vestige for his contribution of defending the town from Devil Riders until he finally falls by Butcher Rose's hand.
Involvement
After Vault Hunters arrived Vestige and wrecked havoc in the bar in an attempt to find the sheriff, he finally show up and quickly put the situation under control. However, Devil Riders invade Vestiage again shortly after. Despite the best effort of the sheriff and Vault Hunters, Butcher Rose still manage to reach the town square.
As a last-ditch effort to fight off the Riders, he and Rose have a showdown but unfortunately was bested. Rose then forcibly takes the stone from Vestige through use of Telezappers, but not before fatally shooting the sheriff in the chest.
Lying on the ground and dying, he gives his badge to Vault Hunters and tells them to find Juno, who will be the new sheriff of Vestige.