The Bed Sheet can also be hung over the bars of your cell to block the guard's view inside.
Night patrol guards will remove the sheets if their opinion of you is below 30.
There is a second type of bed sheet that can only be seen when completing a favor to retrieve a stolen item from a character's inventory.
The only visual difference from the ordinary bed sheet is the blue color, similar to that of the infirmary bed sheets which are unable to be removed. It cannot be used like a regular bed sheet, but can be used to complete the favor to find a bed sheet for someone.
It can be obtained without completing the retrieval quest by exiting and re-entering the game.