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Bioaccumulation!

Some companies are looking at this for nickel mining: grow trees that leech metals out of the soil and end up with metal concentrations that are competitive with ore!

Back of the envelope calculation using the data from article.

To take soil from the Australian residential guideline for soils of 300mg/kg to the article recommended 117mg/kg, you need to remove 183mg/kg from the soil.

The average lead content in the eggs was 301µg/kg, so 183mg/301µg = 608. Meaning, for every kg of soil in your backyard, you need the chickens to lay 608 kg of eggs.

This will clearly take many many many years.

It doesn't go away by itself, but you can of course physically move it (including ingesting it).

It isn't literally true that it never goes away, or you would be right that the eggs couldn't have lead in them, but my understanding is the amount removed by chickens is pretty minimal as a fraction of what's there