Why do sealed plastic bottles of pop collapse as the contents get old?
It is most likely the CO2, H2O and air in the pop bottle headspace diffused (leaked) out of the pop bottle.
You are correct: the pressure has reached ambient (not dropped below ambient). Because the pressure in a freshly bottle pop bottle was originally higher than the pressure in the room (normally atmospheric pressure), and the bottle's plastic walls were smooth and strong, any decrease in pressure inside the pop bottle would cause the pop bottle walls to collapse.
If the bottles were left longer, the CO2 and water would continue to evaporate from the liquid phase until the headspace contained approximately the same pressure as the air in the room. If somehow all the water evaporated, you'd be left with sugar and a bunch of other solids (that were dissolved). I doubt full evaporation of water would occur. 


Also, if the bottle is made from PETE (polyethylene terephthalate), prolonged contact with water (including pop) will result in many by-products. Two of them are:

a. UV exposure, air and water (together) promote peroxide formation on polymer end-groups (OH, COOH). Another way of saying this is that the bottle walls degrade.

b. The PETE plastic could leach some trace antimony (if that was used in the polymerization process) and/or phthalates, suspected to be endocrine disruptors.

IF water permeates through the bottle walls, it can allow for microoganisms to diffuse in/out of the bottle. You might get some mould in there!

Those are just some things that could happen.