It also depends on the kind of PE firm. The vulture firms will buy a stable firm and load it up with debt doing stock buybacks and then cash out and let the company crater.
Other firms, like Texas Pacific Group, are turn around specialists that take struggling firms and fix their business processes to make them run better and raise the stock price by actually building a better company.
There are a lot more of the former than the latter, mainly because it takes some uncommonly smart people to run the latter kind of fund and just a bunch of bean counting jerks to the run the former kind.
Your first example is very old school thinking. When a company 'craters' it's not like everyone gets off scott free. All of the people holding the debt, usually big, savvy banks, with the senior tranches of debt have gotten wise to this sort of behavior. And when I say they've gotten wise to it, I mean they got wise to it 20 years ago. In short, if you want to load it up with debt that the company will never pay back and give yourself a big dividend you first have to find someone to lend you that money. If it's obvious to you that that's a bad idea it's obvious to the banks as well.
Most exits in PE are either going public (in which case you have to convince the equity markets that the company is stable), selling to a strategic buyer (e.g., if Apple were to buy RAX from Apollo), or even selling to another PE firm which happens all of the time.
The point is that neither of these scenarios turn out well if you are levering a company up to an unsustainable capital structure.
They own for-profit education companies like University of Phoenix. Read up on their history, especially the law suits, to get an idea of what the management's values are like: https://en.wikipedia.org/wiki/University_of_Phoenix
That's actually a different firm called Apollo Group (which is mostly comprised of Phoenix and a small number of other things) – Apollo Global is a much larger private equity firm with a confusingly similar name
It appears that Apollo Global is part of a consortium that bought Apollo Education Group earlier this year [1]. Looking at the press releases, those appear to be the two Apollos in question. Though, I suppose you should give them some time to see what they'll do with it.
Other firms, like Texas Pacific Group, are turn around specialists that take struggling firms and fix their business processes to make them run better and raise the stock price by actually building a better company.
There are a lot more of the former than the latter, mainly because it takes some uncommonly smart people to run the latter kind of fund and just a bunch of bean counting jerks to the run the former kind.