They can’t take real estate with them, and there’s no reason why a foreign owner of real estate can’t be taxed more than a local owner. Dividends of stocks in local businesses can still be taxed, as can transfers of ownership of those stocks on the local stock exchange. They’re also dependent on the state they left for any governments bonds they own as well as for enforcing any loans local legal persons owe them.

They can sell all those things, of course, but that just means other people have to start paying more taxes.