Cookies4kids,
I think I know what you are talking about, when I move daylilies I often see this, but I am not really sure it is part of the plant. I always clean that stuff off before planting, and I actually think that is could be fine root material from other plants. Does that make sense? I can just pull the fine fiberous looking stuff away from the plant, leaving a nice clean plant to be planted.Do you have any type of invasive plants that grow in your daylily beds? I always envision those fine roots as invasive weeds trying to get established in my garden and I try my best to remove them all, but that is based on no fact at all. That stuff could be part of the daylily plants, but as you say some have it and some don't.