Keilim, Chapter 24, Mishnah 13. This chapter is built out of a long series of threes: for one type of utensil after another, the Mishnah lists three versions of it and tells us how each version behaves with regard to tum'ah. One version is susceptible even to tum'at midras, the tum'ah a zav or niddah transmits by sitting or lying on something; a second version is not fit to be sat or lain upon, yet it is still a functioning utensil, so it can receive ordinary tum'ah such as tum'at met; and a third version is not a utensil at all, and remains completely pure. Our mishnah applies that pattern to sheets.
The Mishnah opens: "Sheloshah sedinin hen": sheets fall into three separate categories.
Bedding: a sheet meant to be slept upon
"Ha'asui lishchivah, tamei midras." When a sheet is produced with sleeping in mind, it performs precisely the job that bedding performs, and it therefore belongs among those objects that take on tum'at midras.
A sheet used as a curtain
"Levilon, tamei tamei met." A vilon is a sheet hung in a doorway to serve as a screen or partition. Such a sheet cannot become tamei with midras, since nobody sits or lies on a hanging curtain. Nevertheless, it is not out of the picture entirely: it still counts as a garment, because the doorkeeper stationed at that entrance will wrap himself in it from time to time when he feels the cold. Since it does serve a person as clothing, it is a utensil, and as a utensil it can contract corpse tum'ah.
An embroidered sample sheet
"Veshetzurot, tahor mikelum." This is a sheet worked with embroidered figures, and it was not made to be used at all. It functions as a model: one studies the design on it in order to reproduce it on another garment, much like a sample of a particular picture. Because it renders no service to a person, and it is simply a flat piece of material rather than a vessel or a garment, it is pure from every kind of tum'ah.
So the single item, a sheet, lands in three entirely different halachic places depending on what it was made for: bedding that receives midras, a doorway curtain that is still enough of a garment to receive corpse tum'ah, and an embroidered sample that serves no one and therefore cannot become tamei at all.