Depends on the state - many (most? all?) states let people on temporary visas get a drivers license, and don't tie the period of validity together. But more importantly, since there is no system to revoke a drivers license if your immigration status is revoked, a drivers license can only be used as proof that you were able to show legal status in the past, not that you have it now.
> and don't tie the period of validity together
That seems... foolish? Like allowing a root/intermediate CA to sign leaf certs to be valid after their own expiration.
Not exactly. It's more like, your email account at work doesn't automatically deactivate when you die. They're totally separate systems with different requirements.
Some states (like California) allow illegal immigrants to still attain driver licenses.
If it's a Real ID, then the federal government has a database with the documents you used to get it so they can quickly see your US or foreign citizenship and easily find your record from there.