I'm not sure if you're joking or not but corduroy is a fabric of twisted fibres that, when woven, lie parallel to one another to form the pattern of a "cord" (basically it's ridged velvet 'kay). So, sleeping on a pillow made of this fabric would cause small indentions to appear upon your face in the same pattern as corduroy.
If this was a joke then sorry I am a loser.
But seriously, I didn't know what corduroy was...