1966 cent... what caused this error inside and around the rim called?

Maybe this a retained lamination error?

 

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Sorry, but its' damage. It looks like it was repeatedly tumbled, which forced the soft copper to thin and fold over. You can see how the thin layer as folded over the letters near the rim. Usually see this on dryer coin, but your coin only has it on one side.

Laminations are caused by impurities in the original ingot prior to rolling the strip. The rolling process elongates them, so you're not going to find a round one, not is it going to follow the exact diameter of a planchet.

 

I was born that year , I'm damaged also .