Not if you get your assets out of the country *before* renouncing your citizenship.Of course such a plan might mean that you'd risk arrest if you ever tried to enter the country again.
This reminds me of one of a true story from my business days. A European senior finance executive of a mid size privately held multinational company was sent to the US headquarters for an assignment. He was one of the executives with a significant ownership stake. Near the end of his US assignment the company was purchased by a publicly held US corporation. The executive received shares of common stock in the US company for his shares of his old company. The transaction was not considered taxable until he sold shares of the publicly traded company. He asked for and obtained the shares in certificate form, not electronic.
When he was reassigned to Europe he flew to an offshore country for a vacation before flying home, carrying his paper stock certificates with him. While there he sold the stock and deposited the proceeds. The transaction was not taxable in the US as he was not a US citizen and was no longer working in the US. The transaction was not taxable in his native country because he received the shares while in the US and he was not yet physically back working in his native land. The sale transaction had to occur in his native country, while he was technically a resident, to be taxable. As he had not yet arrived home from his foreign assignment he was not technically a resident for tax purposes. The offshore island nation did not tax the transaction because it was happy to have foreign money flowing through its banks.
A unique situation in which timing was perfect to avoid millions in taxes without breaking the law.