What would you do if you managed to come across someone else's private key and it's worth an amount that most people would 'prefer not to lose', assuming you have no [idea who it belongs] to or [location clues]? Eg. Sweeping through common books' text for BIP39-based keys.
I suppose you could send a dollar's worth to a different address and hopefully they'd get the hint.
Honestly if it happens to me and I see the amount is something that I cannot prefer to lose, I'll do everything to make sure I delete the trail and make those coins mine. You can say you should be honest and all but let's face it practically most of us are going to do this, it's human nature, but yes If i was rich enough to not care about the amount in the wallet I would let it go. It obviously all depends on the amount and obviously the amount will be different for everyone.