The company must have more than 500 equity holders and have more than $10 million in assets. If the company maintains a limited number of owners, they will never be required to go public regardless of their valuation.
https://www.investopedia.com/terms/f/forced-initial-public-offering-ipo.asp
There is no requirement to ever go public, in the US anyway. I work for a multi-billion dollar company that’s entirely privately held. It just tends to happen because it’s the best way for the equity holders to convert their ownership into cash. It can be hard to sell a whole company because that requires someone to go all in to buy it and they must accept all the risk of maintaining its value. But you can go public and get tons of investment money without having to sell.
(early) reddit was the answer to the question “what if anyone could have their own phpbb instance without having to host it?” Then along came Lemmy asking “what if anyone could have their own reddit instance and have to host it?”