What should I do about a book I took as a trust from the school library, which has been lost, and its owner has not asked me for it?

If a book is taken as a loan and is lost due to negligence, then compensation is obligatory by consensus. If it is lost without negligence, then you are still liable for compensation according to some scholars, such as the Hanbalis and Shafi’is, who cite the hadith: "Rather, a loan is guaranteed." The Malikis and Hanafis differed in this case, relying on the hadith "There is no guarantee on the borrower who is not negligent," which has been weakened by scholars.

Thus, if the loss of the book is due to negligence, compensation is obligatory by consensus. If you were not negligent, then you are still liable for compensation according to the more preponderant opinion. Compensation is made by purchasing a similar book and returning it to the library, or by paying its value if it is unavailable. The value is determined by experts. The lack of a demand for compensation does not waive the obligation.