Probably not. Because generally personal items such as sheets and quilts are thrown away directly after use. Of course, I don’t throw them away casually. I often need to change sheets and duvet covers due to weather conditions throughout the year. If I don’t change a set, my mother will clean it and put it at home to collect it until the next season changes. Cover it when you take it out. After using it for a while, if it feels old, just throw it away without letting others recycle it. It will definitely be older by the time it's time to throw it away, and there's no point in recycling it.
Few people will reuse such close-fitting covers, especially second-hand ones, which will not be of much use after recycling. In short, no one will recycle bed sheets and quilt covers.