I have shrink wrapped prints and posters up in my storage loft that have been up there for around eight years. Prior to that they where on display at my Midway store and some of them even date back to my old store on Sports Arena Blvd. Total time dates back to the 1970s, up to 30 years.
My storage loft gets downright hot in the summer, over a hundred I would guess. This is San Diego, so they get chilly in the winter, at best.
I have seen no oily residue nor anything else that I would call all that detrimental to the prints that have been stored this way. My guess is you got a hold of some cheap shrink wrap, or that by remaining in the rolled up state, a chemical reaction of some sort, occurred.
It is also possible that some where along the line, someone just spilled some oil on the roll, assuming it was standing on end.
I do remember having an old roll of shrink wrap someone gave me. About the first twenty or so feet of the role was unusable due to just dirt and a foggy look if I can remember right, no oil though.
Look on the cardboard roll that the shrink film is rolled on. You may be able to see who the manufacturer was. If you are that lucky, assuming it is someone like 3M, I am sure they will replace the roll for you.
John