You created a situation whereby an individual who doesn't want to sign the contract cannot stay, however, due to external circumstances the individual cannot leave either.
You think your example is great and you are so smart and you really put Voluntaryists between a rock and a hard place; I think your example falls far short of your target, and I will tell you why.
You state that this community is the only habitable place on the entire planet; this would necessarily indicate that the people in the community are the only people alive. This indicates -because there would be no more importation of food or resources- that the people are going to have to spend their time growing and acquiring their own food more-so than worrying about who signed some piece of paper, not to mention being able to monitor all of the land or serve on a jury.
In a situation like you've laid out, just try and get someone to give-up time -which could be used to procure food for themselves and their family- to serve on a jury because someone didn't sign a piece of paper. Have fun with that. Like in all End-Of-The-World scenarios, government disappears because there are more important things to do, like food production and acquisition.
The Contract becomes null and void when nobody is willing or able to enforce it.
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