This test probably represented the worst case scenario. It was a physical machine in a remote office with no other server to move the repository to. I suppose if I really wanted to save the backup chain, I could have sent an external drive down there and moved the backup chain to that. It wouldn't have been the speediest of fixes, though. We have the data shipped via DFS-R up to a central file server that is backed up by VBR. So, the local chain was lost, but we are still protected.
Thanks for weighing in on this. I just wanted to make sure that I didn't overlook something. The best practice is to have low disk space alerting set up, but this kind of thing can happen if the admins are not attentive to those alerts.