I doubt the pieces of jacket are from actual jacketed bullets, but likely just pieces of copper plating from plated bullets. The plating process for bullets has come a long way since they first premiered on the reloading scene about 35 years ago. It was common then for plated bullets driven faster than 1200 fps to strip themselves from the rifling inside the bore and simply tumble downrange. Bullet platers slowly refined their processes and things got better. Plating got thicker. Casting alloy got harder. But not all bullet platers evolved at the same pace. Berrys and Xtreme have survived because they adapted best and quickest to solve the issues.
One of those issues was shedding of plating under higher CUP or PSI calibers. The phenomenon isn't as bad with calibers that operate at lower pressures like .380, .45acp or .38spl which are all below 20,000 CUP. But 9mm and .40S&W for instance operate closer to 35,000. And 10mm runs at 38,000 or so, as does 9mm+P. I noticed that it was not uncommon when cleaning up muzzle brake ports on IPSC guns that ate a steady diet of plated bullets to find bits and flakes of plating that had fused to the baffle surfaces. I can easily imagine that if the owner of that can shot a lot of plated bullets, a lot must have accumulated inside there.
For decades I stayed away from plated bullets because of these shedding issues, and because I wasn't aware the matter was improving. About 10 years ago, upon discovering how much better plated bullets had gotten, I began using them on a limited basis, but still only for subsonic loadings. When I would disassemble a suppressor to clean it, I did still find some copper plating flakes, but not a distressing amount. It did concern me however that, copper being harder than lead, over time, the blasting bits might prematurely erode the baffles, so I limited my suppressor ammo to truly jacketed only for the longest time. In the last 5 years, I've become a convert to the polymer coated stuff for suppressor ammo. They are often at least as affordable as plated, but usually cheaper, and reduce internal deposits of lead as a whole.