A magazine article implied black exhaust smoke can be caused by the mixture being either overly lean, or overly rich . I can see that for overly rich, excess carbon from the excess fuel, but how could overly lean cause black exhaust smoke?
As far as I know, it can’t
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I agree with @Mustangman
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When a hole forms in the piston. Good news- it doesn’t persist very long 
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An old time way to tune a boiler (coal or oil fired) is to start with excess air, (lean but inefficient because air is heated and sent up the smoke stack) The operator then slowly trims the air intake down until they see smoke in the stack. Then gently open up the air in take until the smoke stops. A good operator could make a boiler operate very efficiently this way.
A lean mix, excess oxygen, burns all of the fuel (no smoke) but is inefficent as heat is wasted by sending too much warm air up the chimney. A rich mix, excess fuel, does not burn the fuel well, resulting in incomplete combustion yielding lots of smoke.
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Lean mixtures burn fuel inefficiently just like rich mixtures and can cause black smoke from the incomplete combustion of hydrocarbons (HCs). The mixture has to get pretty lean though. HCs increase the richer it gets from 14.7:1. HCs decrease as the mixture gets leaner, until about 16 or 17:1, where they start to increase significantly.