This might be a weirdly-too-specific question about US passports and the State Department to be answered here, but I couldn't find a forum that was a better fit. Since it involves an airline, I'll give it a try.
I lost my passport between JFK and home (the DC area) while traveling this summer. I immediately contacted American Airlines, JFK, and DCA. Both airports got back to me - no luck - and AA sent a form e-mail saying they were looking and would be in touch. I had a flight to Canada two weeks later, so I declared the passport lost and got a new one. American continued to send me occasional form e-mails saying they hadn't found it.
This morning I get a text and e-mail that my passport has been recovered. (Thanks, passenger who finally checked the seat pocket in the last row, I'm guessing.) I'm relieved it's been found. I click the link in the e-mail to get the details. Turns out it was recovered at DCA - where I could have picked it up this weekend - and then sent to American Airlines' lost luggage facility in Dallas. There's no pickup option and the cheapest shipping they list (3-day Fed Ex) is over $20. Which seems like a lot for something small, flat, and invalidated.
My question is this - if unclaimed, will American Airlines eventually send my passport to the State Department? And if they receive it, will the State Department send it back to me or destroy it? I'm probably going to bite the bullet and pay, as my passport had some stamps I'm fond of, but I'm curious as to what airlines are legally required to do in the case of government property.