Um, no. Private equity is not what you're describing, and is the opposite of how Warren Buffett operates.
Private equity specializes in leveraged buyouts of companies. The typical deal is that the private equity partners put their own money into a fund, that they then get others to invest in. This fund puts up a downpayment on a company with the bulk of the loan being taken out by the company, and then buys out the current owners. The private equity folks then try to "put lipstick on the pig" by making the company generate what looks to be good numbers, and then flip it to someone else. The profit is then shared with the fund as returns.
Sometimes the deal goes wrong and the private equity partners have to run the company for longer than expected.
Sometimes the deal goes very wrong, and the company goes out of business. Like happened to Toys "R" Us.
Even when the deal goes wrong, the private equity partners typically make their investment back between the fee for setting up the deal, and fees for running the company. This leaves the investors in their fund and the bank holding the bag as everything crashes and burns. But hey, that outcomes just proves how much smarter the private equity guys were than everyone else all along!
Compare and contrast to Warren Buffett's approach of buying whole companies cash, keeping current management in place, and running them for long term returns.