The City Reformatory was a prison-like building in the Lower City. The building was made of worn looking dull grey stone and had several barred windows and a large, imposing door with a sign above it reading "City Reformatory" in Nosgothicletters.
The Reformatory was probably aSarafan prison, given its imposing structure and barred windows (and heavy usage of Sarafan banners nearby). Indeed, if Kain approaches the door, screaming can clearly be heard from multiple people, along with the sound of a whip cracking[BO2].
Since Kain found Sebastian feeding literally right next to the building, it is possible that the inmates are, or were, fed to him and possibly the other vampires who served under the Sarafan.