I think gp was referring to how capital gains aren't taxed until realized. Having billions in unrealized gains gives you influence, even though you didn't yet pay tax on it.

However, when you relinquish your citizenship you pay an exit tax which is more or less equivalent to what you'd pay if you sold all your assets and paid gains taxes, so I'm not sure how this move really helps billionaires, except that they don't have to pay taxes on future gains.