I think the question of what to do about the ring is tough and there are no firm answers. You make your own rules.
I'm not taking mine off my left hand until the state says the D is final. Then I'm moving it to my right as a symbol of our friendship.
She lost her ring a year or so ago and recently gave up the search and filed the insurance claim. She's trying to save the $ but has ended up spending some of it on bills and car repairs. It's so sad to see such a beautiful thing wash into the everyday mush of bills and expenses. I knew this would happen sometime because she was always taking the ring off and forgetting where she put it, like misplacing car keys but more important. I was bitter about it because it was such a unique ring. I never said anything about it during the year it was gone but then again I never offered to search for it or provide a replacement (even temporary). Now look where that got me.
"My actions are my only true belongings. I cannot escape the consequences of my actions. My actions are the ground upon which I stand." Thich Nhat Hanh