Firstly, the citizens of Rome were in three classes, according to the property they owned – the Patricians (richest); the plebs (spread across a spectrum of very rich to subsistence farmers, and the Proles (unpropertied – prole = breeder, a bit of a joke on that was all they were useful for).
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So the plebeians by definition they were not out of work – the Censors conducted a censorship every few years to check on people’s classification and reclassify them as necessary.
So the plebs were not out of work; if they lost their means of subsistence, they were reclassified as proles.