I understand a lot about narcissism, but this is one aspect I can't quite figure out. My ex also has extreme NPD characteristics and had the exact same attitude in regards to property, blatantly just keeping things not only that didn't belong to her but some things for which she had little or no use.
And a ring? Yes... she was given an engagement ring a year before she left (we never married, as well), but didn't return it. Actually, I didn't even mention it for about year, following the tradition that "a gentleman doesn't ask for it back, but a lady never keeps it".
When I finally just noted that she still had the ring, she blew up, as if she had been waiting for the very word to be mentioned every day for a year! I casually asked why she wanted an engagement ring from a person whom she never intended to marry. Her reply was a defiant: "One day, this will be for my daughter!"
Now, I've never been accused of being a genius, but that claim has never made much sense to me. Plenty of mothers give daughters their wedding rings, but I cannot imagine at all what sentimental value an engagement ring from someone she hates and never married would have.
My only guess about the whole thing is that it's simply yet another act of "control", a strong NPD characteristic. Of course, an NPD would want to legitimize their desire for control, so maybe the whole "it's for my daughter" claim is simply that... an attempt to put a benevolent face on a belligerent act.