I think they call this a retained struck-through, but now it's not "retained", so... I would be very careful with the black piece so it stays intact. Did it just fall off the coin or did you have to encourage it out? I think I've seen these somewhere with the piece struck-through encapsulated along with the coin. I'd say it's fairly unusual for a piece this large to stay with the coin, and it will definitely command a premium for the right collector, if that's what this is.
Edit: OK, maybe it's not that uncommon. https://www.sullivannumismatics.com/information/articles/strike-through-error-coins. Scroll down to "struck through plastic".
"This error type is mostly found on bullion, and to a lesser degree on other modern mint products. Struck through plastic coins have a shiny, thin, even strike through which usually has a few straight lines and then is ragged elsewhere around the perimeter of the strike through. We know these coins are struck through fragments of plastic because many coins have been found with the plastic still retained in the strike through. The plastic comes from a covering which is used to protect the dies, and is removed prior to the die’s being put into service to strike coins. Sometimes not all the plastic is removed, resulting in a strike through. In the silver eagle show above, the coin strike through is very shiny (almost like the mirrored fields of a proof coin), and it is a classic example of a struck through plastic."