You get a personal check from nana, you sign the back, you lose it?

No.

It's theft. And an easily identified form of theft (since the person had to sign the check and put it into their own bank account).

Finding a check is not the same thing as finding a random $100 on the sidewalk.

In that case, the "law of finders" would apply, meaning that absent the appearance of a rightful owner (who in this example could not be identified) then the finder becomes the rightful owner.

But a check is different. It has identifying information on it. It has a specified maker (with address) and a specified recipient (with signature). Anyone who then receives/ finds this check, and who was not given the check, is misappropriating the property of someone else for their own UNAUTHORIZED use.... which is textbook larceny/theft.

100% legal? well obviously it's fraud, but there's not a whole lot you can do about it.

BTW, a third party endorsement typically requires that you, the payee, write "pay to the order of," or "for benefit of," or at least "FBO," with the printed name of the third party. If the bank allowed that check to be cashed without this written information, it was a bad move on their part, and if the person who stole your check wrote it, it was forgery.

In cases like this, banks usually just pay out the money if you provide a police report attesting to the circumstances. It's much cheaper for them than paying an investigator or lawyer to chase it down. If your check was under a thousand bucks, just call the bank and get the details on securing a refund.

yes. in some jurisdictions, you might have a civil cause of action against the person who found the check -- 'unjust enrichment' or similar. unless the check was large, it isn't remotely worth the cost of the attorney to bring the suit.

but the banking system will have nothing to do with you claim and Nana won't get the money back from the bank.

I think so, but either way the time/money spent to pursue this issue is probably not worth it. Sucks.....