Here's one type of gun made by a few different companies....
Takedown Carbines.
Often called Takedown guns or sometimes Takedown rifles. But carbine is the most accurate description. Most are .22LR in caliber. But .410 gauge and even 12 gauge shooting varieties exist. The classic AR-7 in .22LR is one good example (still made today as the Henry Survival Rifle). Unfortunately the .410 gauge Garcia Bronco all-metal shotgun that separates into two pieces and is very inexpensive, is out of production. Ruger has a Takedown variation of their 10/22 model. There's the Taylor's 1892 Alaskan model in either .357 Magnum or .44 Magnum. It's a lever-action carbine made in a modern-day materials way.
Unlike the AR-7, many modern-day Takedowns are closer in design to the unfortunately discontinued Springfield Armoury M6. Making for a very compact package. If you can find one in good shape, the M6 with it's dual barrels that fire .22LR and .410 gauge is worth considering. Though nowadays you'll likely pay a large premium for one.
Many Takedowns separate into two pieces. You simply screw the barrel assembly onto the stock. Though I don't like that arrangement. Same reason I don't like compact outdoor stoves (designed to burn wood) being made in multiple separate pieces that you have to assemble. Lose one piece, and your stove is now completely useless.
Some of you are likely saying, "There's still the matter of weight and bulk in even a large BOB."
True! Absolutely true. With some of the Takedowns, that's true. Still, they're good car-carry emergency survival and Bug-out guns. Plus, a couple can actually fit in a large BOB pack with a minimum of bulk and not too much weight. The two best ones would be the aforementioned Henry (AR-7) along with the little skeletonized Chiappa Little Badger (folding) model. You can't get more minimalist that the L.B. (though the Henry is going to be more versatile).
The L.B. is a single-shot .22LR (.22 Magnum or .17 HMR models exist too) with the ability to hold spare rounds inside its skeletonized stock. Only negative being (outside the ones of its very design) is that Chiappa is not known for outstanding quality. Better-than-decent quality to just good quality. You're not getting Ruger 10/22 quality with this little guy.
Also keep in mind that Takedown guns, while they can be pressed into service for that role, are not made for self-defense against 2 or 4-legged predators (with the 1892 Taylor's model being the big exception to that). These are outdoor survival guns made for small-game hunting. Rabbits and similar sized critters for your cooking kit that you packed in your BOB. Yes, an AR-7 is better than nothing in a self-defense encounter, (and why I think it's a better choice than the L.B. for packing in a BOB) it's still very far from ideal. Especially in a scenario where regular medical services are non-existent for now or possibly for a very long time. Keep that in mind if you have the option to flee but instead choose to stay and shoot it out with armed adversaries, instead.
A Takedown is still worth considering. Especially in a large BOB with something along the lines of the Henry or the Chiappa mentioned above. Chiappa has other Takedowns too. One is a spiritual clone of the M6.