... to answer whether a society can cease to exist is very real, and it happened to the Olmecs and the Mayans and even to Rome.
Another issue, which no one has yet addressed, is whether handguns will be more important than long guns? As you move through vast areas, a long gun will stick out and draw attention to those carrying them. Handguns are discreet, concealable.
Once one is established in a new location, long guns rule. But on the move, long guns can turn one into a threat or a target, especially if any roving criminals or LEOs are trying to round up guns.
+1
My choices, assuming they can be transported, are:
1. Handgun of established reliability and familiarity of use, revolver or pistol, in 38sp or better. I think the 9mm is the best option for the kind of situation under discussion, and I selected a Glock.
2. .223 carbine, Mini 14 in my case. With red dot for defense and variable power scope for hunting.
3. SKS or AK of confirmed reliability.
4. .22 rifle or handgun, 10-22 for me.
5. Bolt action rifle with good scope. Am leaning towards K-31 with St Marie mount. In a societal breakdown I'd have no qualms about permanently modifying my Finn M39 with a scope mount; it may be more reliable over time than the K31, and more ammo may be available for it (though I agree with those who keep enough ammo on hand, rather than hope to acquire it).
If I had to start selecting among these (on the move with no vehicle), I'd probably keep those higher in the list. #2 and #3 are backups for each other, and I'd really want one of those and a handgun. I don't list a shotgun because I don't have one. I do realize a shotgun may be the most versatile and pragmatic choice of all.
That the family portrayed in the program were woefully unprepared was probably intended to be a lesson to viewers. It was clear enough that those who were surviving were not afraid to wield firearms. The traveling salesmen were well armed and portrayed in a very positive light. The lawmen in the town where the kid was caught looting and shot? Neither unrealistic nor entirely condemnable, and though no one knows how they'd react in such situations, I hope I'd be able to muster up the necessary mercy to let the kid work off his crime.
If something like that ever does happen, the sheer volume and variety of toxics, including radiation, in the environment are going to make survival a lot more a matter of chance than preparation. Preparation is a necessary but not sufficient condition for surviving a total societal breakdown. I do think those who know how to grow food would be among the most valued of community members after the first year, a point made in the program I do agree with.