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Status for a library item that cannot be found, is currently charged to a user, but the user asserts that it was returned to the library.
Most libraries have specific circulation policies for dealing with such tricky situations. The library may be at fault, such as from a failure to check the item back in -- in which case the item is usually found on the shelf and replacement fees can be given. However some users re-shelve their overdue books rather than returning them in an effort to avoid late fines. The user may also be mistaken about having returned the book, either intentionally or not.
Some libraries offer receipts to users returning books as an added protection against unexpected claims returned situations.
A comparable situation in banking is known as the "empty envelope deposit," wherein a customer initiates an ATM deposit with a blank envelope, then withdrawals the unsecured funds from the fake deposit, essentially obtaining a free loan (or theft) until the envelope is opened. Libraries, like banks, have fairly strict rules against such deceptions.