Employees with private company shares have very few actual rights; this is almost part of what defines "private companies".
It's not a stupid question. There are a lot of misconceptions about employee startup stock; it is, to an extent greater than commonly imagined, really just a glorified profit sharing plan.
The reason for this is that your (hypothetical) company isn't trying to create a broad market of investors in its equity. Rather, it's trying to express an incentive that allows employees to share in the upside of a liquidity event at the company.
This issue is distinct from vesting. Even after you've vested, the company is unwilling to yield control of who owns its shares. The company is fine with you parting ways and retaining your upside interest (in fact, it's happy you did!), but not fine with you selling the package that gives you that interest.
For obvious reasons, the story is totally different at public companies.