I just purchased another "sleep cap" because the elastic in my current one has loosen.
It is actually an extra, extra wide headband. I like the texture in them because I do not want my locks to be completely flat. If my locks are already curly, the grooves of this textured headband keeps the curls in place. I just stuff all my curli-locks underneath in a circle around my head.
I can only find these double wide headbands in the private beauty supply stores for about $1.50 USD.