The potential problem lies beyond the processing plants and distribution. Prior to these steps in the chain, you begin with farmers and ranchers. Many of them depend on continuity to keep their operations going. If they can't take their poultry, pork, or cattle to market, they don't have room (not enough barns, pens, etc.) to keep and feed the animals while simultaneously breeding the next generation of animals. So many chickens and pigs are simply left to die or terminated; just like pouring milk on to the ground. And if the problem persists, some of these people go out of business. If that happens, you have a supply problem at the source (the farm) resulting from the present problem at the second stage (the factory).
Farmers are smarter and more resilient than you give them credit. For generations farmers have lived their lives and managed their farms in crisis mode pretty much all the time....droughts causing crops to fail or not have enough food to feed animals.....too much product causing prices to fall...hail killed their crops.....it goes on and on constantly for farmers.
A problem with liberals in general is you think farmers are a bunch of stupid rednecks who can't figure it out. In reality they are a pretty smart group who always figures it out to survive and pass the farm to the next generation while at the same time supplying everything Americans need.
Prices will be volatile until it all gets sorted out but they will get it done.