Defraggler's verify disk utility is a wrapper around chkdsk and its /F parameter.
I don't know how to recover the deleted files (and if they were deleted by chkdsk...they probably were unreadable anyway), but...your drive seems to be in a bad state. If it simply is a backup drive, format it and backup everything again - and if that happens again, buy a new drive.
A quick Google search for "chkdsk deleted files" returns lots of failed attempts at recovering files. As I already said, if chkdsk deleted them, there had to be a good reason to do so - here's one : http://www.techspot.com/vb/post414691-12.html