Can the N360_Backup directory be limited in size?

I have installed, a couple of months ago, a new 5 TB external drive for all of my backups and archived files.  I then directed my 360 backups to this new drive.  The backups run OK without issues.  But when I tried to move about 800 GB of files I wanted to archive, it errored out saying I didn't have sufficient space available to move the files.  Checking properties of the disk drive showed that there was over 4 TB used already.  I went to my archive directory and it was only 250 GB used.  Checking the N360_Backup directory I see 0 bytes used.  Apparently I'm not allowed to access this directory.  Is there a way to limit how large this directory can be, so I can use the disk for other purposes ?  Or if this shouldn't be happening, what can I do to correct the issue ?