In A Tree Grows in Brooklyn, the last chapter is similar to the first chapter except the protagonist is now a grown woman. For example, in the first chapter she watches the older girls prepare for their dates by washing under their arms; in the last chapter she herself is performing this ritual and another little girl is watching her.
Is there a particular term for this device? Wikipedia suggests framing, but to me that’s when a narrative goes on within another narrative (like Frankenstein). I suppose in musical terms it would be a reprise, but I’ve never heard that term applied to a literary text.
If it helps TV Tropes.org has called the article “Book Ends” and further specifies the situation as you described it as “Here We Go Again”. I think (but I can’t be sure) that at least the first of the two terms was in use before TV Tropes used it as the name of an article.
In addition the term “callback” has an article, covers the situation you described and which I’m convinced was in use before TV Tropes.
Bookending was also the first term that I thought of. I know I’ve heard the term used to describe the device before. A Google search reveals:
“Mirror” what you did in the opening. Some people refer to this as “bookending” your speech because the content of the closing is similar to the content of the opening. That doesn’t mean you say the exact same thing, but if you began a humorous story you could close with another humorous story. Or, if you began by reading literature you might end by reading other literature.
