I've been using TAR since the 1990's and have built many disks from tapes and drives.
I think the problem is a compatibilty issue with TAR from Fedora 16 and Fedora 23.
I copied the F-16 tar to the F-23 system and it doesn't work: when I try to use it the system says "file not found".
I can't get into the system - but I came up with a trick: I put a cron job that would send an xterm session to my F-16 box, so I could talk to the F-23 and do some testing - but the cron job doesn't fire up. I verified my coding by putting the cron job on the working partition and it works fine, but doesn't run on the broken partition.
I'm wondering if there was some changes made to the filesystem structure.
I'll look at the timestamp of the backup and then search the broken partition for anything that was changed after the original build. I can probably find all the things I did to customize it - especially disabling all the security features.