No, that's not what bankrupt means. Bankruptcy almost never happens when there is literally zero value left. In the archetype we're discussing, there is enough value in the company to pay the banks and PE firms lavishly and exorbitantly, but not enough to do that and keep the company healthy (or indeed, alive, in countless cases). So the PE firms choose just the first one.
> Assuming the company can pay off all their debts
This, too, seems to be unfounded assumption that turns out to not be correct, as explained above.
OK, so there is enough value in the company to pay the banks and PE firms lavishly and exorbitantly, but not enough to pay all their debts. So which debts can they not pay?
> Assuming the company can pay off all their debts
This, too, seems to be unfounded assumption that turns out to not be correct, as explained above.