The volatility isn't removed, it's just not being printed every day. A non-traded REIT owns the same kind of buildings a public REIT owns, and if office values drop 20%, the value of those buildings dropped 20% whether or not anyone quotes a share price. What changes is the mechanism for setting the price. A public REIT's price comes from buyers and sellers trading all day, so it moves with market mood as well as with property values. A non-traded REIT's price comes from appraisals on a set schedule, usually monthly or quarterly, so it moves in smaller steps and lags.
So what you're buying isn't stability of value. It's stability of the reported number, plus insulation from the moments when public markets punish an entire sector regardless of what individual buildings are doing.
And @arbor named the cost. Your exit runs through the sponsor's share repurchase program, which is typically capped and can be suspended.
Two terms to keep straight, because people use them loosely. Public non-traded REITs register with the SEC, publish audited financials, and are generally open to any investor, often with minimums around $2,500. Private non-traded REITs are exempt from registration, restricted to investors who meet income or net worth tests, and require a lot more diligence on your part because there's less mandated disclosure. People say "private REIT" for both. They're different products with different protections, and it's worth knowing which one a given offering actually is before you read another page of it.