I don't even know if this is possible. Is there a process in the minting that would create a reverse rim? Instead of thicker it is thinner. I know this coin had a hard life and is no beauty queen. The coin weights 3.12 grams and that seems inline with my other '56D's. Any help is appreciated. Thanks.
It looks like it as encased in something, that's why the funny rim. Somebody who probably needed the money took it out.
Correct. That cent is damaged. As stated.. It was encased in a lucky cent holder or bezel. Not a mint error of any kind.
Growing up, lucky coins were a cool thing for young boys around my area to have on a key chain (easier to carry than a rabbit's foot). Sometimes the coins would wiggle loose, but a quick squeeze from a pair of pliers would rectify that. Encased coins came in a multitude of holders. Businesses gave them away and you could get them as souvenirs from visiting places like Niagara Falls or Pike's Peak. There are even groups that collect the older or more obscure ones.