It just looks like the fibers that remain attached in the crown area from dead leaves/scapes from the previous year(s) with a bit of green staining from an algal growth of some sort. I wouldn't be concerned with that stuff, except that it appears the middle of the clumps have died. I would guess that any live roots in the area belong to the nearby live fans. The only way to really know would be to dig it up.
It looks like you might have them growing through holes cut in weed barrier fabric with rocks on top. I'm thinking that maybe the weed barrier and rock combo works so well that it prevents the daylily clump from naturally expanding, so instead it grows somewhat congested (on top of itself even it looks like?) and maybe some varieties in that situation will tend to choke themselves out at times... or it leaves them too exposed and vulnerable in winter perhaps. You would just need to divide them occasionally and sink them back down in the ground if that's otherwise working for you.
I hardly ever need to divide a daylily in my garden, but every garden is different. (I have sandy soil, rarely fertilize/water--basically mine are neglected once they're established--so that could be why!)
