I can't speak for the specific case of Stripe, but it's fairly common for private companies to have a "tender offer" in which employees have the opportunity to sell some portion of their equity. This is often done in conjunction with a new investment round.
There's a newish term for this: RLO, Recurring Liquidity Opportunity. These are tender offers at some recurring interval. Even some companies that have a shorter lifespan (say 7 years) offer this.