I mean, we're running up against one of the problems which metadata systems have to deal with, which is that metadata about an object really "lives" in parallel with that object, and not really "contained within it". But usually you just think of an object as containing all of the metadata we know about it so far, and under that model this makes perfect sense.
To do this in 100% RESTful style you would therefore probably store details about how an account was closed in the /accounts/440278/closed reference, so a PUT is correct, with GET /accounts/440278/closed returning either a 404 for accounts which are not closed or else the metadata about how the account was closed. This could live in parallel with a cache that's on the resource itself describing whether it was closed or not.
So, POST or PUT, with the PUT exposing more of the metadata interface to REST and POST putting more of it in the request bodies themselves.