Part of the issue is the TYPE & LENGTH of disaster we would face. I think all of us who have animals/livestock have given thought to short term problems, evacuations and such. Newbies, not so much...

they just haven't had to think about it yet. Next would be time of year and where you live, major problems in some areas. Lastly, time of warning, if it was a disaster like that.
If every store closed...what do you do?
I'm with most of you....the chickens would broaden their forage area, not as many eggs? Maybe, maybe not. Mine free range all day now, could do without day end feed. Winter has less bug, etc., but still enough when they dig. If I had snow on the ground for 6 months, different story.
My dog & 2 cats -- I generally have several cans of their food & dry foods. BUT they will eat human food -- eggs, meat, dairy & veg. My dog is a 10# min pin.
Goats...if in milk, there's more for all of the above. Still make cheese. The goats can go into about 125 acres of wooded bliss behind me...another couple hundred to my North. They will follow me like the Pied Piper. So I could take them out like a shepherd. After all, if I can't go to a feed store that means I'm not going anywhere.
My old minis would be a little bit of an issue as a couple are old enough (33 & 35) to have jaw teeth gone & do well on their sr feed. BUT...will eat some softer foods and I could make that happen and that's only a couple of them. I have plenty of pasture that hold other 16 of them & goats for 8-9 mos a year, plus several power right of ways if hay were short supply & time when pastures were down - winter. They are hot wire trained.
Life FEM says, much depends on the time of year. Winter is harder for some areas, yet most of us with animals try to stock our hay for the winter in quantity. My farm is in a crop farming area, back to time of year, could be huge assist if I needed to buy some, or graze winter wheat. In desert area -- heat & water, plus very limited natural forage.
Obviously, I could take a deer (there's plenty here every night) but, it would last years for my cats & dogs.

Lot of wild turkey around. There are streams, rivers & lakes for fish. Walk or bike there. I don't do fish but chickens, dog, cats do.