There are reinforcing fibers that automotive tire manufacturers advertise made of steel and kevlar for higher performance tires. Kevlar is plastic and IIRC was invented in the 60's.
From riding a bicycle as a hobby, most of my puncture flats on the road come from tiny steel strands that come off of tires that have been used a little too much. I imagine the steel fibers just rust away eventually but the kevlar just gets ground into tinier and tinier bits.
>Rubber is also considered plastic, both natural (isoprene) and synthetic (styrene butadiene).