Why would anyone bother to renounce "their" citizenship? I'm not going to assume you are the property of a government-- a "citizen"-- unless you publicly affirm that you are. Who would do otherwise?
How can a person renounce something they never explicitly agreed to or embraced?
If a crazy person imagines she owns me, is it necessary for me to publicly confirm that she doesn't?
If someone imagines I'm a dog, do I need to renounce my status as a dog?
If someone has gotten it into their head that I'm a brain surgeon, do I need to file papers proving I'm not one?
Now, if the crazy person is going around announcing to everyone I know that I am their slave it might inspire me to say "No, I'm not", but if the delusion exists only inside their head what is it to me until they act on it?
If someone else gets the idea that I belong to Crazy Cora or a government, or that I'm a dog, the problem is obviously theirs until or unless they act on it. Other people's craziness isn't my responsibility.