That is the problem with not allowing users to delete files from a network share. Microsoft office creates temp files when it opens up files for editing. When it closes it needs to be able to delete these files. Without the right to delete these files the files will be left in the folder. You can try adding in the delete for the owner. This is a special right that can be granted. Edit the security of the folder, and add the user OWNER. Grant this user the right to delete files. This way users can delete the temp files which they create. They will also be able to delete other files which they create, but it will solve your temp file problem.
You can also enable shadow copies on the folder. This will tell the server to make a copy of all the files on the server every <i>n</i> hours and it will keep <i>x</i> copies of all the files. It requires a bit of hard drive space to do this, but it will help you in the event that someone deletes someone as you can recover the file from the last shadow copy that Windows took.
————from Jonathan Hassell
[b] The shadow copy suggestion is meant as an alternative to preventing delete on a share.[/b] It’s a good one, too, as shadow copies (also called Previous Versions in newer editions of the operating system) make it very easy to recover from accidental deletions. This is my recommended best practice.