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So what did you think about the ball melted matter that left a trail across half of the last pillar ? Is this a one of a kind error coin or are there others like this one . Because no matter were I search I can't find one .
Again, it is not melted. The blanks used for cent planchets then were punched out of 95% copper sheet stock and after upsetting and rinsing were sent to be struck. No melting involved once in the Mint's possession.
Here is a cent listed on
http://www.cuds-on-coins.com that has similar die chips on the columns in the same area:

It is listed as IDB-1c-1970D-01R and can be found here:
http://cuds-on-coins.com/lincoln-ce...b-1959-2008/Yours is a different year but, the same process resulting in the same sort of die chips/breaks seen on the example above. Yours is larger and that indicates a later die state when the original die crack continues to break away and cause successively larger chips/breaks on the coin itself. It's a progression of deterioration where the longer that die is used, the larger the break becomes and it is transferred to the coins struck.
Take a look at all the other coins listed there and you can get an idea of what breaks look like.
Die chips and breaks have a fairly recognizable shape to them if you've seen enough. Yours is definitely that and is not the result of a hardness test or melting of any kind.
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I also have another strange coin that has the circle of the number 9 in the date almost completely filled in with more coin .
I'd be willing to guess (not an expert) that what you are talking about here is a
Wheat cent and most likely from the 1950's. It, of course, happens in other years but it seems to be most prevalent in that time span. It's called a "filled number" and is actually a small die chip on the protruding piece of the die that creates that depression in the 9 on the coin. There are also "filled letters" and it's the same thing, just in a letter.
Here's one I have that is a "BIE" cent (1957-D) and has a "filled" B. These are two die chips:

In Memory of Crazyb0 12-26-1951 to 7-27-2020
In Memory of Tootallious 3-31-1964 to 4-15-2020
In Memory of T-BOP 10-12-1949 to 1-19-2024