Usually, they'll have to, since such stock is usually conditioned on you granting the employer the Right of First Refusal (i.e. the chance to beat any offer from a buyer you find).
Check your stock agreement. I worked somewhere it didn't just grant first right of refusal, but the company had to _approve any sale_. In practice, they approved almost no sales, so this was a ban on selling shares before IPO.
This seems like an interesting dynamic because the company has to balance getting a random outside shareholder vs having to buy their own shares back for whatever price you negotiated.
You do not need a formal market for stock to be stock. A share of stock represents ownership. You are confusing that with publicly traded stock markets.