That would explain the 벽 in 벽장!

The closet is in the wall. This is a really weird sentence in English. Did the wall swallow it? Is it like a Harry Potter wall? Otherwise, it would be through the wall (still sounds really odd but makes technical sense), built into the wall, or part of the room (which might be what's implied). Oh, final option that I've never seen in a real life home but could imagine—The closet is set into the wall. (inset like an alcove with a hanger bar and some other features) Does the Korean phrase sound sensible?