Post-1982 pennies are made of copper-plated zinc. America uses this composition because zinc is cheap, but zinc is a terrible metal to make coins from because it is highly reactive - you don't even need strong acid, it will literally dissolve in the rain. The copper plating protects it somewhat, but if the plating is stretched thin, worn away, or gets little pinholes in it, then the zinc will rapidly corrode underneath the holes.
This is what has happened to your coin. "Zinc rot" is the usual coin collector term for it. And if you want to see more coins that look more or less just like this, then search the forum for "zinc rot", or ask any metal detectorist to show you their penny finds.
So in that sense, your initial assumption was correct - it has indeed been "eaten away by acid or something like that" - except the "something like that" was most likely just plain old water.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis