The way Files and FAT works is similar to a bookcase (files) and a library (FAT). When a book is taken out (file deleted), it leaves a space on the bookcase. In that open space you may be able to fit one book, or two books in its place depending on how big it is. Depending on how many spaces/gaps you have, you may be able to slide/cram all the books to a side to generate more space for a big book to fit in. Cramming the books like this is similar to "defragmenting" a computer, which moves all data closer to itself making a big area of empty space instead of multiple gaps where books used to be.
Even though the space may be empty from someone taking the book, unless the Librarian scans the book, the system (FAT) will think it's still there/occupied. This is probably what happened in your case, and oftentimes FAT will have issues knowing what its truly free space is, especially on removable drives. Without using the "safely remove hardware" feature, the FAT may become corrupt or may not have finished writing everything.
Running chkdsk (right click on the drive, go to Tools, then "Scan Disk") or doing a format should both resolve the issue, I suggest backing what files are there up in both cases, as chkdsk may just replace the FAT.
