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 of business" - then it shouldn't be a tough decision to make.
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 of business" - then it shouldn't be a tough decision to make.