A supply chain is still a supply chain, it has raw material supply, process labour, warehousing, and distribution. When you have the local economy shutting down due to all this panic, supply chains are stressed even if they are local. Add then on top of that you have the supply and demand production schedule. So when you have the ridiculous sudden demand, the system wasn't design to cope, the "supply chain" breaks down.
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good pic. This is a good visual representation of most modern day retail chains. Food industry looks similar - especially when you get down to minor ingredients like herbs, spices, colours and flavours. Many of them are processed overseas closer to where the farms are.