Returning library books can present odd problems.
Some years ago, our library sent a book to an Ivy League college on ILL. These loans were usually for six weeks. We didn't get it back even though the college insisted that it had been sent. We had to write that book off as lost.
Several years later, it turned up. It had been deposited in the book drop of public library branch. The strap identifying our library was intact and the branch returned it to us. What actually happened is still a mystery.
On another occasion, we received a book we had sent out on ILL. The spine was broken and whole signatures had been removed. It was a complete loss. When we contacted the library we were told that the book had been received in that condition.
. We would never have sent out a book in such a bad state. We did eventually get reimbursed for that one but it took a long, long time.