Companies absolutely can "disable" trading by certain shareholders. This is what an IPO lock-up is, where insiders cannot sell their shares until 6-12 months after the conclusion of the IPO. It's also what a trading blackout is, where employees cannot trade shares between the end of the quarter and release of earnings. These are
very common - almost everyone who works for a public company has encountered them.
These cases are temporary, but I suspect there are also permanent trading bans that might be caused by legal action - if, for example, an employee is found guilty of a crime, or is under a wage garnishment order.
Also, crypto has long had the phenomena of coins that get "locked" and can never be touched or transferred again, simply through holders that have died or lost the private key. For example, the original "Satoshi coins" - the roughly 1M Bitcoin (~$45B at today's prices, enough to make their holder the 27th richest person in the world) mined by Satoshi before Bitcoin became mainstream - have never been spent, and it's likely that their owner is dead. They simply drop out of circulation, and the price of all other Bitcoin rises to compensate.