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Humans have survived on Earth without infrastructure or farming for most of our existence, so even if the worst happens I can see some people surviving if there are enough natural resources left. It would of course depend on hunter / gatherer skills, which most people do not have, but are totally learnable.

In the book Sapiens by Yuval Noah Harari - he even suggested that hunter gatherers had a far better quality of life compared to someone living in a farming society. Obviously what we have now is far better than either.