Joanna, I will try to help you. The fact that the stems have roots is pretty common for species lilies. Mine do the same. Some grow little bulblets on the stem that can be detached and planted. I have some bulblets potted up now. I do not think you have killed them. I would replant them as soon as possible, then cut off the stems at ground level. I haven't dug mine in several years and probably won't unless the start to lose vigor. I have noticed that a couple have passed on , but that had set bulblets in the ground which will bloom when they get big enough. I read on one of the lily threads, I think, that some people plug the hollow end of the stem with a little glue to prevent winter rains from sluicing down to the bulb and rotting it, but I haven't tried that. Eventually by spring the remains of the stem will degrade and will be easily removed. I wouldn't try to split them right now, I
would put that on the garden list for next year. I think they need to go back in the dirt now because winter is nearly here. I use popsicle sticks to mark where mine are so I don't dig them up when I am planting spring bulbs.