His brother was Ezrolith Churn, who later went on to become Archchancellor of the University.
Eliaz held a seat on the University Council, as befits the head one of the eight orders, and also took part in the Rite of AshkEnte when the Archchancellor demanded they summon Death so that the reaper could explain why the Octavo had activated and cast a change spell encompassing the disc.
Death's information was worrying - the Octavo had cast the spell to save Rincewind and the last great spell that he was carrying from being lost over the edge of the Disc. Oh, and that the world would end in less than a month if all eight spells were not gathered together and read.
Along with all six of the other orders, Eliaz dispatched a team of wizards from the Last Order to hunt and catch Rincewind in the Forest of Skund. It did not go well, as the rival teams fought with each other in their haste to capture Rincewind before the others.
Eliaz found that further attempts to locate Rincewind by magic failed, and the orders were unable to recover the last spell by the deadline. In the end they acquiesced to the new Archchancellor, Trymon's plan to read just the seven spells instead.
Eliaz died, along with the other order heads, when Trymon was taken under the control of things from the dungeon dimension. He was turned to stone, and his statue later moved into the University grounds.