It's not a business model solely used in the states, it's global. The deals are called Leveraged Buy Outs.
Let's look at Pizza Express.
It's been bought and sold multiple times (by private equity firms), and very little equity will have been put into the sale each time and will have been funded by debt.
eg Pizza Express is valued at £250m. The new owner might give the old owner £25m which they have available and the remaining £225m will be paid to the owner after they've raised the money against Pizza Express. It could be bank loans but more often than not, it's from other private equity funds.
These loans will come with interest and of course these need paying. Each time a restaurant chain gets sold in this manner its profit margin gets eroded to the point where it's so thin the only way to keep it going is to increase volume of sales; or open new restaurants.
It only takes a slight increase in running costs eg after the Brexit vote ingredients from mainland Europe became more expensive, or a dip in cash flow and the whole thing, to be quite frank, is absolutely fucked.
It's a great way to buy a business without using much of your own money. When it does eventually fold the people left on the hook are the creditors- the people who loaned the money to finance the purchase.
This is indeed how the Glazers purchased Manchester United. People kicked off because loads of £ every year goes to financing the debt and isn't reinvested into the club.
Sorry for the long post, turned into AK for a bit there