I do not have access to a scanner so please hang with me. My "Penny" is about half as thick as a regular penny. It is worn but the features are worn about the same amount. There is no rim. With it being so thin it is bent somewhat. Is this an error or do I have a plain old strange penny?
Sounds like an "acid job". The coin was immersed in a corrosive liquid that eroded the surface. Such coins are characterized by: 1) thin or absent rim; 2) a complete design that is uniformly fuzzy; 3) design perfectly centered; 4) diameter smaller than normal; 5) very thin. Sounds like your coin has most or all of these hallmarks.