They usually do well for two reasons. First, the debt is on the books of the company they take over, not the private equity firm. Second, once they have control of the company they charge it 'management fees' for the executives and consultants they assign to run the firm.
They’re also free to loot assets: e.g. one popular technique is to transfer things like real estate and then have the former owner rent its stores back. At the end, they have that property to sell with none of the obligations.
Oh I wouldn't count on that. I'm not sure in this case, but PE usually has a way to "win" even if the company does not.