The Dog House is a cryogenic prison within Sector Seven that was designed by Kokonoe and used to contain Azrael. The prison itself has temperatures so low that anything within it has their movements completely restricted. The prison earned its nickname as one of Azrael's nicknames is Mad Dog.
Sector Seven temporarily released Azrael from the prison, and after being thawed out, he treated it as if he had just awoken from sleeping. Azrael did not return to the prison until Jin Kisaragi and Kagura Mutsuki managed to defeat him. In the new world created by Ragna the Bloodedge, Azrael was returned to the Dog House. Kokonoe has constant surveillance over the prison. 
BlazBlue: Central Fiction Library Entry
- Cryogenic Prison
The place where Kokonoe confined Azrael for two years. The temperature is so low that it even restricts the motion of atoms, and completely stops those inside form moving.