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You need to determine who owns the debt. Sounds like the collector was only hired to collect and does not own it - if they owned it they could make any deal they wanted. Call the library back, get a contact number for the accounting dept or circulation manager (whomever is responsible for accounts and sends them to collections.)
Request that they pull it back from collections, accept a payment if there is still a balance (evethough they say there is no longer a balance), and request that they delete the reporting.