The glass closet idea was publicised by Eve Kosofsky Sedgwick in her book 'Epistemology of the Closet'. A 'glass closet' is an open secret, specifically, an open secret regarding one's homosexuality.
It is possible to define two types of glass closet: either someone is clearly homosexual but refuses to come out, or someone is out to some people but not to others (most gays for most of their lives, probably).
The actor Kenneth Williams and composer Benjamin Britten can both be regarded as glass closet cases.
Alternatively, a really fragile
piece of furniture, for displaying your collection of designer clothes