Private firm - no public trading of stocks.
Private equity - a business model created by syndicates that borrow money to buy companies, saddle the companies with that borrowing, demand a quick return (-> layoffs, selloffs, and wage cuts), then bankrupt the company when all the value and productivity have been extracted.
It's the sub prime mortgage thing all over again
Spirit was created and sold to the investment firm (Onex) in 2006, and Onex turned around and sold its the last of its stake in Spirit in 2014. Onex got over $3 billion for their initial $375 million stake in Spirit. The cost, as we're rediscovering, is that quality of Spirit's product went to shit and the long-term viability of Spirit is in question.
Fact that it sold for more doesn't mean it was in good shape. There are many potential reasons why people would pay more, even if Spirit was in bad shape.