Is there ANY WAY that BE can delete files that are in use during a backup

I ask this question as I'm having very bizarre issue. I have one server where twice a file was being used a week ago. Then yesterday they come to me and it's just 'gone' (we all know this). the funny thing is that the whole directory the file is in is being backed up, no files are being left out. A restore job doesn't show the file being there even up to a month ago but I know it was there as they were using it. I only ask this as for some reason i've yet to be able to fix my SQL machine this file is on fails every single time on my Incremental backup so daily I have to do a full. I thought BE skipped open files (in case it was open). Again, don't need a solution per se just wondering out loud. Thanks!