You legally can hold shares of any company, but you'd have to spend insane amounts of money. Even when companies are acquired the shares aren't actually transferred to the acquirer. One of the custodial companies just merges the shares into the acquirer.
As an example, I used to own a couple of shares of both Apple and IBM. My shares were held directly in my name by computershare, which is the transfer agent for both companies.
When I sold them, someone _probably_ bought them through a brokerage, which means that computer share updated the registration to name Cede & co as the registered owner of the stock, and cede updated an entry indicating that the buyers brokerage owned the shares, and the buyers brokerage updated an entry that said that the buyer owned the shares.
This is irrelevant - a US brokerage cannot arbitrarily trade your shares, whether or not your shares are held in street name.
> GP could probably purchase the shares and be issued stock certificates that they could physically own, in which case there would be no chance of a brokerage being able to sell them.
This is equivalent to suggesting someone put their cash in a mattress rather than using a bank. The real solution is to find a better bank.
Indeed. It seems most people think the Hypothecation agreement on a Margin account is something brokerages can do without having such an agreement on file. They can't.
But you're right, if you care to not trust that, you do have the ability to either get certificates (if they're issued for the stock in question) or do a direct registration (DRS) so they're held directly in digital form at the Transfer Agent. Just of course bear in mind that if you're NOT intent on holding these shares forever, selling at this point can become a multi-day process, so you become a bit less able to react quickly to market activity.
GP could probably purchase the shares and be issued stock certificates that they could physically own, in which case there would be no chance of a brokerage being able to sell them.
(I'm not disagreeing that the brokerage's action was sucky, mind you)