I'd really like to know the answer to this as well. From all the research I've done in the past 10 minutes, you'd think that plastic is simply immutable and indestructible, and that even after millenia has passed it will still be plastic (even if in smaller pieces). But the Google SEO on this is dominated by environmental groups trying to emphasize the short-term life cycle of plastics, and it's hard to find anything with a longer-term perspective.

I think if you wait long enough (billions of years) then the landfills will eventually be under miles of earth and subjected to high enough pressures that they fundamentally change; in the same way sedimentary rock can change into metamorphic.