This also applies to things they lost last semester (the spring semester) and have found over the summer. I will refund monies up until September 30th. (This is my own PERSONAL policy. I cannot speak for other librarians in DISD.)
However, in October it is time to take care of this matter. Children can either pay for the item, come to the library and work it off, and various other choices that I give them on a paper which requires parent signature and the choice they want their child to follow to take care of their outstanding library account.
Also, there are some district policies in place where books are forgiven at certain grade levels, for instance from 2nd grade to 3rd grade, if you had a fine and had not taken care of it you are given a clean start.
It is a fine line between wanting students reading, no matter what, and yet also wanting them to be responsible and accountable for things that they borrow....this is a life skill. Please converse with your child (if you haven't already) about being considerate for things that you borrow from other people or places. The library is an excellent source to further that conversation and build that life skill in your child. :0)