+ I don't think this is going to be a DIY process. We're looking at north of $20K considering filing fees for renouncing, GC, naturalizing again and all legal fees. Also it's likely going to take 8-10 years to complete, realistically.
@ac8238 are you sure your family member is ready to go through this lengthy and expensive cycle full of unknowns just for the checkbox?
Also, does your family member have a different citizenship to fall back to? He / she cannot renounce US citizenship to become a stateless person. If he / she obtained the citizenship based on asylum it becomes extra interesting.
That would make a good book / TV show for sure.