This faction is mainly concerned with providing a common set of dialogue responses for its members. Having all the jailors in one faction also means it's easier to stop the members warning each other off the locks and so on.
The purpose of this faction is unknown. Beyond owning Jair's Shack and its door it does nothing else and contains no members. Jair and Isleif the Open Handed simply never lock the door to the house.
Apart from keeping the Jemane brothers on good terms, this faction is used only to set up the ownership of Reynald's house in Chorrol. It is never referenced by any scripts, which means that Weatherleah will always be available to the player as a location in which to sleep.