Question

how could a society without property operate​

Answer 1

Hunting and gathering forest produce would be the only activities in such a society as there would be no initiative to go into agriculture and produce a surplus. It wouldn't be a socialist society as well. Strong people would be able to feed for themselves but the weak will depend endlessly on their loved ones.

Answer 2

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Its only in socialist economies that societies could operate without owning any property. In a socialist society, the state owns factories, lands, banks and other resources.