The system is a self hosted solution on Ubuntu Desktop 16.05. I may not have the MariaDB backup file (or even if I do, it may be a few months old), but I should be able to get access to their harddrive and all the contents on that.
Is there anyway I can re-create their instance from that information?
You can try to restore the hard drive to a new system. Once that is done and you are able to start ERPNext on it and if the data is available in the DB then you can just take a backup and restore it on a new server.