Ohhhh a live one! Sir do I have a wonderful bridge in Brooklyn to sell you! :)
Fun fact: banks fund this sort of nonsense constantly. I've asked about this before: why they do it. They must be making money I just don't know how. The LBO guys pay themselves massive management fees and dump the debt on the company so they walk away scott free.
My wild guess was the banks offload the eventual IPO onto investors and so make their money on the IPO fees and funneling their own clients the dead-man-walking shares. But I honestly don't know.
The banks get paid back their debt when the next PE fund buys the company or the company pays it off. Unless an IPO is being done to pay off debt, which it never is, the mechanism you describe doesn’t occur.