> they were relying on reports generated from a data warehouse which incorporated a copy of that MySQL database and was being populated by an undocumented, not-in-version-control cron script running on a PC under a long-departed team member's desk.

This definitely happens but at some point someone with authority needs to show technical leadership and say "you cannot do this no matter how desperately you need those reports." If you don't have anyone in your org who can do that, you're screwed regardless.