What happens to PET if it is dumped into landfills?

It will stay there, inert, similar to glass.  It will not degrade biologically; one of the reasons it is such a good choice for packaging foods is its resistance to attack by microorganisms.  It will be crushed flat without fragmenting (no shards) and occupy less space that the more rigid glass.  It is resistant to the chemical species found in landfills and will not give rise to any harmful leachates.  Indeed, these very properties are utilized in stabilisation of landfills and processed baled PET bottles have been used for stabilisation of the foundations for road works.