Prisons and more specifically prisoners are massively profitable to their jailers/owners no matter if they're private, state, or federal. Even private corporations are profiting from the US prison system. The federal government runs a corporation called FPI/UNICOR which sells out prisoners for profit. States also have programs or companies that lease their prisoners out to private companies who pay those prisons (or the government) a lot of money to get an endless supply of workers who can't complain about working conditions or being paid pennies a day (almost all of which goes back to the prison anyway). Some prisoners are forced to work for no pay at all.
Prisons will let people who are supposedly so dangerous that they need to be locked up and denied parole out of jail long enough to work their shifts at fast food restaurants, retail stores, plants (like Tyson Foods) and warehouses and they'll run their own companies inside the prisons themselves like call centers which get contracted out to private corporations or government agencies for a profit.
Some prisons also run farms, modern day plantations, that use slave labor to sell millions of dollars worth of food and crops to corporations whose products show up in our stores. Whole foods, kroger, walmart, and target all sell products made by prison labor. Food and crops raised on prison farms even get exported to other countries.
Inside the prisons everything prisoners get they have to buy from the prison which overcharges them for everything. The workers make pennies but the markups on what they need can be 600%. The commissary vendors are for-profit and the prisons get kickbacks from them to get exclusive access to the captive customer base. Private companies partner with prisons for release cards and make profit from that. Phone calls from prisons can cost over $20 for just 15 minutes (https://brilliantmaps.com/jail-call-cost-usa/). The US prison system is designed to make money. Private prisons tend to make more profit on their prisoners, but so do state and federal prisons, the vendors they employ, and private corporations. Of course even while the government and corporations rake in money taxpayers are still on the hook for a lot of unnecessarily expenses, including the costs of policing and the court systems that feed the prison system a steady stream of new and returning prisoners. Everybody knows that we could save billions in tax payer money is we focused more on keeping people out of the system, but there's profit to be made from slaves so no one will fix it.