A book cage refers to closed stacks that are locked off from public access by virtue of being placed inside a gated room (which usually looks like a jail cell). At the New York Public Library, this collection was often referred to as the "triple star" collection because all the call numbers started with "***." (Search CATNYP, the catalog of the research libraries of the New York Public Library, by call number using "***" to retrieve a list of these items.)
Prison libraries often have locked or restricted areas, such as in the Elmwood facility in Milpitas, CA, where hardcover books are locked away.
In past eras, libraries sometimes physically chained the books to a lectern or shelf.
In the television series Buffy the Vampire Slayer, the Sunnydale High School Library has a notable book cage.
Hogwarts School Library has the infamous "Restricted" section that Harry snuck into (while wearing his invisibility cloak) to find out information about Nicholas Flamel.