I can see being liable if you take the found jewelry and don’t report it but don’t see how you would ever be liable if you just left it there.
That’s the point. You aren’t liable if all you do is keep on walking. So that’s what I’d do. It’s not so much “theft by finding” as it is “theft by finding and taking, intending to keep forever as yours, even though someone else owns it and might otherwise have the ability to recover it if reasonable steps are taken by all.” But that’s a bit long for a wiki title.
Oh, and, uh, IANAL.
The last time I found a wallet on the sidewalk downtown, I took it to the police station nearby and they acted like I had stolen it and gave me the third degree. It was weird and made me really uncomfortable, and I wouldn’t do it again. So just ignoring it is probably what I’ll do if it happens again.
A woman I know was cleaning homes a few years ago. She “found” a baggie filled with white powder under the couch. For some reason she put the baggie into her purse, then stopped by to ask me if it was what she thought it was.
The bag held just a bit over a half ounce of cocaine (I tasted it). She kept the baggie in her purse for two weeks, then put it back under the guy’s couch the next time she cleaned his home.
I found an envelope with $2700 in cash and checks worth $4000. I was unemployed at the time and had about $3 on me. There was also a deposit slip in the envelope so finding the owners was easy. The money belonged to a couple that had just held an estate sale for their son, he was killed in an auto accident. I gave everything back and told them it would have been real easy for me to have kept the cash and toss the rest. They gave me a generous reward and gave me some work around their house so I had pocket money. We also became friends, they later turned into one of my biggest fans when I resumed my stock car driving hobby.
TMI, Dude. Just keep it to yourself.
I hope she got rid of that purse after that. Imagine coming up on a situation where there are drug-sniffing dogs, and a woman who is quite possibly an immigrant, and therefore Must Be A Cocaine Mule.
A close friend actually did find a diamond ring once.
She kept it.
Of course, she found it IN HER TOILET AT HOME (how’s THAT for an incentive to keep up with the housekeeping!!). She was scrubbing with the toilet brush, heard a clink, put on a glove and went fishing - and came up with something shiny.
Best theory: a former resident of her condo, or the one upstairs from her, lost it somehow. It got stuck in a pipe somewhere, and for whatever reason somehow it got jarred loose. IIRC, she did ask her neighbors, and she had no contact info for the former condo owners (she’d lived there for several years at the time).
Huh, I’ve turned found stuff in to the police twice, and both times they were nice abuot it.
Once, it was a piece of gold jewelry found on a college campus. Not my taste, but enough gold to be worth something, and worn enough to look like someone liked it. I took it to campus police, who maintained a lost and found. I called them a week later, and it had been claimed. The other time it was an expensive car key, attached to a house key. No car, and I don’t think there was any other info. I called the police in the town where I found it, and they said to bring it in, so I did. I didn’t bother to follow up on that one.
Those Canadians! 
You already told us that story. To be fair, it was in 2014!
My wife has several pieces of very expensive jewelry. Last month I finally got around to sending the list to the insurance company. Before I did that, the policy had a cap (I think around $5,000) for jewelry. So, don’t assume it’s insured.
And I also reject your premise that the insurance company paying a claim so someone can keep a bracelet they found is a situation where “nobody loses.” (and I hate insurance companies)
I was pretty sure I had - but it definitely seemed appropriate to this thread 
That’s truly bizarre, the police treating you as if you’d stolen the wallet.
Did the wallet have any cash in it? If not, maybe they decided you’d stolen the wallet, taken the cash, and in a display of misplaced and rather twisted morality, decided to turn in the cards themselves to the police.