Closet i think is a very ggood word for it. Not everyone can come out in fact some are probably better staying in for sake of mental health and conflict (i know thats controversial) but I do think closet is a very good word for it all.
A closet is a closed, cramped space, with very little space to breath never mind be yourself and filled with clothes and fabric we wear or hide behind.
Iv come out to some. My biggest shock has being the love Iv gotten and the freedom i feel.
I do worry though that my trust might be misplaced though im still glad i did it!