different worms "spit" out different types of this "silky" stuff. have you seen a featherduster worm, or christmas tree worm? or any other type of worm like these, spins a cocoon like cylander to hide in and they put there "crown" or feathers out to catch their meals. well they use this web like substance to hide them selves and as a protection. if they are bugged or you try to move them they will spit this junk everywhere. it coated my whole tank one night. i couldnt see in the pic but from how you described it tht is waht it seems like.
i attached a pic. but the stem is the silky stuff when it takes form. but when used as a defence, or just when you move it the excess comes out it is a nasty web like substance.