Technically, you can still own them, I believe. However, …
A new 10% withholding tax is imposed on distributions made by these companies. The new withholding tax doesn’t fall under the double tax treaty and therefore you won’t be able to claim it back when filling out tax returns. You’ll still pay the full Swiss income tax on the distribution (no 10% deduction).
Additionally, you’ll pay 10% tax (to the IRS) when you sell the company (regardless whether you made any gains or losses).
See this video for more details: https://www.youtube.com/watch?v=SCWCYxeXuQk