Let's say, while cleaning house clutter, someone discovered an old library book (borrowed, say 35 years ago) from a library that no longer exists. Can he keep the book?
Assume that there are no heirs or other take-over companies / orgs. that can be located. Heirs MAY exist, but you have no way to find out. Similar idea with the library. Perhaps, there is a parent library that took over but after a viable investigation, you couldn't discover what or where it is.
Updated based on comments
There is a discussion regarding the concept of Yi'ush, meaning if the owner has given up hope of getting his item back, it is considered "ownerless" and the finder may keep it.
To consider in your answer - Would the principles of yi'ush apply in, say, the case of a library book borrowed so long ago that by now, had the library existed, no one would recall the book was borrowed (the loan pre-dates computer databases in libraries. They were still using index card catalogs!) and since the library doesn't exist, now, technically, there is no "owner".
(Above is an example. Answers should be general to similar situations.)