"Until the Constitution is revoked by consent of the people, it and all the laws passed under it remain in force."
We must be sure not to equivocate either 'force' or 'law'. I pointed out the many meanings of the latter above. But to say that the law will be 'in force' in a PAW because it is on the books is to not emphasize the difference between de jure
and de facto
: for just because a law is on the books and it is to be followed by its force de jure
does not mean that such a law has any forcede facto
Without an organized power to enforce law what is written in a book or on a piece of paper is pretty much worthless, or as Hobbes says, "covenants, without the sword, are but words and of no strength to secure a man at all." In a PAW, indeed, even in everyday practical life, what is written about your rights in a book means little at the point of impact of a criminal's club if you are too weak to defend yourself or if you live in a state where armed defense is prohibited. The facts on the ground will determine in large measure what will be acceptable or unacceptable.
In as much as preparing material goes, disaster prepping is perhaps fun if not cool if not paranoid. But that's the easy part. To be prepared also means to be prepared morally, politically and psychologically. There will be some who contain a democratic spirit and will cooperate; then there will be bandits and criminals who scavenge just as they do now; but there will also be megalomaniacal tyrants who will aim to become feudal lords or dictators. Nor can one assume that all our former neighbours will only want to be peaceful, law-abiding democracy lovers. The Stanford Prison experiment and the Milgram experiment showed that people are very plastic given certain facts or situations.
States throughout history have come into and gone out of existence as has their laws and customs. Indeed, the U.S.'s origin itself is a violation of the 'law' in so far as the founders did not want to pay their taxes to the King and so revolted. Somewhere I bet there was a written law in England making it illegal to revolt against the King's commands. Sometimes, therefore, breaking the law is the right thing do (and by 'right' here I do not mean 'legal' but 'moral'), assuming representative democracy is better than hereditary monarchy. Of course, what is 'moral' is a discussion to be had; but even this notion is not without its own history of debate so even if it is not admitting the exactitude of geometry it is still not undefinable.
The fact remains that the difference between legal, moral and natural law can set up a system akin to that of a trump card: one would think that natural and moral laws will trump mere legal laws (and the civil rights movement and the abolitionist movement is a case in point in the absence of a PAW); I doubt that one could expect such trump power to diminish in a PAW. Of course, stealing another's property is not illegal because there is a law against it; it is illegal because it is immoral for people's property rights are natural, not merely legal.
Of course, the scale in both time and space will affect things greatly for the first people in a disaster will still have some of the values and principles of the old system and there may be some outside help to keep traditions alive; but if neither is the case then after a few generations the old ways will be forgotten. If a disaster is truly a PAW the state system that was before it may never return, regardless of one's patriotism.
Still, a state's constitution's existence is not sufficient for the existence of the state: there must also be an organized power that fulfills the duties and obligations that the state owes to the citizen; if those duties and obligations cannot be filled then the state does not actually exist and, by a right of nature, a person resumes his or her natural sovereignty.
Hobbes wrote:For the laws of nature, as justice, equity, modesty, mercy, and, in sum, doing to others as we would be done to, of themselves, without the terror of some power to cause them to be observed, are contrary to our natural passions, that carry us to partiality, pride, revenge, and the like. And covenants, without the sword, are but words and of no strength to secure a man at all. Therefore, notwithstanding the laws of nature (which every one hath then kept, when he has the will to keep them, when he can do it safely), if there be no power erected, or not great enough for our security, every man will and may lawfully rely on his own strength and art for caution against all other men.