This is non-obvious to me. Care to elaborate?
Finance is high wizardry, treating literally every single problem you have in dollar terms, but it built the modern world. Us software developers exist in what's basically the frontier of business. $10 million is just getting started for a software company. But it's enough to push through to profitability in every single other sector.
The key is you have to have it as cash in the bank. You can't finance a turnaround, the better move at that point from a financial perspective is to just fold up the business, but if you have it, you can use it as collateral for a more aggressive expansion.
That way if you run into enough problems, the money guys can 'foreclose' and use the reserve capital to enact a turnaround plan, and eventually earn their money back. It's an extra form of security.
If a finance company is running a business, it's because the industry people that started the company managed to run it into the ground, finance people never seek to start businesses in any other space than the finance space. It's just not interesting to them. When they wind up running companies, they mostly just delegate all the decisions to the consultants they have a working relationship with.
It's simple, you go to a lender who demands you keep $10MM in the bank as a contingency fund. You run the company into the ground, and the lender has to foreclose on the loan, taking control of the business. They then use the $10MM to turn the company around, eventually recouping their investment over the long run.
You're bringing the $10MM in collateral, not the bank, so the bank doesn't have to use their own money for the turnaround. It's a hedge against risk, not some kind of magic bullet like you seem to think. No paradox needs be invoked, the finance company simply runs the company differently than you would, from a purely financial perspective.
Perhaps solving the problems costs $4 million and the revenue is only $3 million.