The Stasis hall can refer to one of a number of rooms on the Ancient ship Destiny with stasis pods built into the walls. There are several such rooms on Destiny and can be presumed to be almost identical to each other.
It is unknown if the stasis pods were ever actually used by the Ancients. After the Destiny expedition arrived on the ship, the rooms were re-discovered by Eli Wallace, Adam Brody and Dr. Nicholas Rush while exploring an unexplored section of Destiny. After telling Eli not to touch the stasis pods until they had been looked up in the Destiny's database, Dr. Nicholas Rush monitored the room from the bridge. When he saw that the pair were indeed working on the pods, he used the controls on the bridge to remotely activate the pod that Brody was working on, while he was inside it. After neither Eli nor Chloe were able to open the stasis pod and release Brody, Rush deactivated the pod. Neither Eli, Chloe or Brody were are aware of Rush's involvement, with the latter two believing that Eli accidentally pressed one of the controls to cause the pod to activate. (SGU: "The Hunt")
The entire Destiny expedition is currently in stasis here (save for Eli, who is fixing the stasis pod he needs to use) while Destiny completes a three year journey to the next galaxy. (SGU: "Gauntlet")