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The only system that can ever have literally 0% unemployment is slavery.

If humans have choice, some will always choose to quit their jobs on any given day.

So the situation you're describing is nonsensical; it's incoherent to try to extrapolate what it would mean because the premises are incoherent.

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https://en.m.wikipedia.org/wiki/Full_employment

This explains it better.

Milton Friedman's "natural rate" of unemployment is basically "the rate capitalists are gunning for" in an attempt to suppress wages. Quite a bit below full.

I don't see anything in that link about increasing unemployment in order "suppress wages". Milton Friedman's comments are about monetary policy. Unemployment can be decreased by increasing inflation, but Friedman thinks thats a bad idea. He not arguing that anyone should "gun" for that unemployment rate, but rather that it should be accepted as the "natural" result of an elastic market.

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