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.
Provided the old hard drive spins up, its contents can be copied to another, to recover all the files necessary to restore the database state at the time of the crash.