"First, I would like to structure this so that all shareholders have a choice. Either they can stay investors in a private Tesla or they can be bought out at $420 per share, which is a 20% premium over the stock price following our Q2 earnings call (which had already increased by 16%). My hope is for all shareholders to remain, but if they prefer to be bought out, then this would enable that to happen at a nice premium." - https://www.tesla.com/en_GB/blog/taking-tesla-private?redire...
If you hold shares in a company that gets bought, your share is converted into your portion of the proceeds. You can't refuse.
In this case, Elon wants to let current investors stay investors, so you should be able to hold your share and it'll convert into whatever the private equity equivalent will be.
The private equity equivalent of a share of stock is...a share of stock.
Musk has already said that you can continue to hold them.