I actually don't see any issue that isn't simply a matter of money. Everything they list that's an issue seems to revolve around the fact that the employees with domain knowledge for the system have left the company. Reach out to them and hire them on as contractors. If they left under bad terms because the business was a bunch of dicks, expect to pay 10x market rate. If this is truly "fix this or the business is out…
Throwaway purely so that I can comment. I've had this happen before. Years ago I left a rather awful company - I left on great terms with my boss, though I hated the company. I was the last person who knew how to release X product. While I documented everything, after I left, the wiki lost its mind, backups apparently weren't a thing, and the director of IT moved to Bermuda. Fast forward 6 months.. a contractual obli…
I have bosses at previous companies that I'd help for free today because they were good to me and we parted on friendly terms. One boss helped me move my house once, and I'm not about to charge him to fix some random issue.
I have other bosses whom I'd require a cleared wire transfer of money before I'd lift a pinky to help them, because they were not nice people and I don't want to associate with them or assist them with anything. If someone in this camp approached me, I'd have a story just like yours afterward.