Your coin may have originally been struck on a thin/light planchet, And then throw in years of wear you get a "light" coin. For a wrong planchet error you would have to prove there where other coin planchet in the mint at the time your coin was made.
Take a picture of the edge. It will be thin thin if it is struck on a light planchet. Also, I kinda want to see.
Thin planchet originally. Add in all those years of wear and you will get what you got. A lightweight coin.
Honestly, I don't think that is thin enough to only weigh 0.38 grams. It is supposed to weigh 3.11. Maybe your scale is off?
It's best to open a new thread, @Tuna - you get more correct responses that way. I was wondering how the coin you showed matches the one the OP posted. Your coin looks to me to have been spooned, or the rim worn down by PMD somehow. The experts will know, though. Edit: And welcome to CT!
Haha, yup. It's really a thing. Saw this one from @paddyman98 himself: https://www.cointalk.com/threads/dryer-coin-vs-spooned-coin.304963/#post-2888999 Although looking more closely at spooned examples, the rim actually increases in width instead of decreasing like this penny shows.
Haha, I guess it passes the time. I remember seeing it in a movie about prisoners - guess there's not much else to do.
Looks out of round and rim is missing. Altered by someone with too much time. May have started out as an attempt to make a double headed novelty coin.
The penny is going to a coin grader to determine content wt. it weighs about same as a 1941 mercury dime. The other 1941 penny large one in same bag. The wheat on back is pulled to the edges. Looks like there is no rim Flip and look at front.