Whilst it's true that an investigation can in some sense be resolved, a case - like Pandora's box - can never really be closed.
To understand why that's so, one needs to recall the etymology of the word case. It derives from the Latin casus, but that's a translation of the Greek term ptōsis, meaning fall.
Thus, case, in a sense, is another word for fate; that which befalls the individual; an innumerable series of events, some big some small, all of which are determined by other events (and not by any external agency).
Of course, the word has taken on extended and transferred meanings over the years, but when I use it in the title of posts - as I often do - I'm not simply using it in a legal, medical, or psychoanalytic sense, but as something impersonal and fateful; something over which the individual has no control (the individual, of course, being an unfolding of events in the same way that the author is a complex effect and function of the text).