This simplistic analysis however ignores that before the buyout the company might have been a prosperous self-sustaining entity fully capitalized by common stock with little debt. That common stock, made into a small percentage of the capital structure by the buyout, is often wiped out too in the event of bankruptcy - indeed it is usually at the bottom of the totem pole in that capital structure. So although they may no longer be majority owners, bankruptcy is typically an unhappy event for long-time stockholders of the company such as founders, employees holding company stock in their 401ks, etc.
Perversely this is the kind of company PE outfits typically go after - in their worldview it is a waste of leveraging potential not to apply debt to such a company. I recommend reading "Barbarians at the Gate" if you are interested in this topic.