Well people don't really know for sure. I think the most correct statement would be to say it gets gobbled up in the kidneys eventually, but how it is hard to say. It is supposed to be biologically inert, however that doesn't mean it lasts forever, and if it doesn't last forever then somehow it gets dealt with. Urinary excretion is probably the primary pathway it will leave you under. It is possible that over time the rugged nature of the body could cause pieces to fall off of PEG, especially if we're talking a big PEG like 20K-40K, and eventually you will have nothing left. Or there may be a low affinity enzyme that can deal with it over time, people just don't know about it. If you are taking something like MGF with a 5K PEG on it, then the total 9kilodalton mass is still way under in the kidney filtration cut off weight of ~40K and while the MGF might circulate for a while, it will just be passed out in urine/feces after enough time (~24 hours probably).
Despite the big PEG craze the biopharmaceutical industry underwent in the past 10 years, it is becoming apparent that PEG does have downfalls and that there are better alternatives for making long-acting hormones in many cases. =)