In Levithania it is recognized that, until 18, a child has no rights of themselves, being owned by the parents. Parents have a duty to raise their children responsibly, and may allow their children to make decisions, but the state does not recognize them as having any rights. If something happens to a child, it is the parents that sue, not the child.
In particular, a child, of themselves, may sign no contract. If a child, for example, wants to get a job, the parents would sign a contract with the employer whereby they agree that the child will work there if they give the child money (which is implicitly owned by the parents) (most parents, being reasonable, make such decisions based off what the child wants).
This all changes though when the child turns 18. The day before every child turns 18, they go to the signing place, at the borders of Levithania. At the moment they turn 18, any rights their parents where holding on their behalf are transferred to the child, and any contracts the parents sign no longer apply to the child (although the child may choose to renew them).
In particular, the child is no longer bound by the laws of Levithania. They are a free person, and temporarily, considered a foreigner. A pair of soldiers stand by them, now in a State of Nature.
They are now officially a person.
A government official brings in a copy of the Levithania constitution, known as the "Contract for the Agreement of Cooperation between Levithanians" or the Contract for short. At school as a child, they took a class on this document, so they understand it fully.
The person now can decide for themselves whether they want to be bound by the laws of Levithania. If they accept, they will read the contract aloud, and then sign it. They are now bound for life to follow this contract (unless some condition specified allows it to be terminated (for example, a legal body given proper authority by the Contract may pass a law allowing citizens to terminate the Contract if they move away from Levithania)), and in particular it is considered just for laws to be enforced against them. They additionally gain the rights and privileges listed in the contract. They are a Levithania. Then they have a celebration usually.
Now, for anyone to truly have chosen to be a Levithania, and the Contract to hold any manner justice, the person is also given the choice to not sign the document, and to remain in the State of nature. This is the ultimate check and balance on the government, the ability of new citizens to not agree to Levithanian law. If this is done, the soldiers escort the foreigner off of Levithania, with any possessions the parents give them, and exile them. They may only return if they go through immigration, which involves a similar ceremony.
The question is, where are they exiled?
How do you exile someone, given that most of the world is already claimed for various countries (think current day Earth). Putting them in another country would violate the rights they have over themselves, since that other country would presumably force them to follow their laws (if the person agrees with that, its fine, but a large number of non-signers want to be anarchists, and won't agree to any laws.)
What can be done with those who decline the rules of society?
Keep in mind that, if the government is currently being very bad, you may have a large number of non-signers. Therefore, we want this to be cheap.
(Backstory FAQ: What happens if you pass a new law? There is a law making process. You don't re-sign for each new law, since you agreed to the law making process. What if you break a law? The Contract specifies that. Probably built-in to each law. Probably fines or jail or what have you. Branches of government can also punish each other, in accordance with the contract. If the government breaks the Contract extremely enough, the people are morally allowed to rebel or not recognize the government, which means the government won't break it too badly. What makes this different from what we have know? It's mostly philosophical, but still in an important way. It gives the government Legitimacy. It's a different mindset when everyone is a signer of the constitution. It's sort of part of their national identity.)