I feel like if there's any value it's in the stones and metal, and those are pretty notorious, even to a non-expert like me, in having Not The Resale Value You Want. And that's assuming it's not fake stones, which I'm willing to believe it is. The dude doesn't want to have much of a relationship with her and then gives her an expensive ring? Or he gives her a costume jewelry ring because of sentimental value. He's already lying to her about who owned the ring to begin with.