Do you have soil that shifts a lot? Have the roots been in the ground for a really long time? Some herbaceous, mainly a few of the older lactifloras, seem to develop more of a woody crown on the root as they mature, I've had some of those more exposed over the years. I've found when it get to that point that stem numbers and flowers have slowly started to decrease so I dug them up, divided and got rid of the woody root part as no new storage roots or viable eyes grew on that part. I had 1 NOID that I loved, cheap bagged root from WalMart, that had to be divided every 5 years max because of that. Hope I still have that one, haven't noticed it blooming yet in AL so can't be sure as I never knew the correct name and didn't put a NOID tag on it.
I assume you're somewhere around a zone 5 in Connecticut? If so and you have viable looking roots exposed with eyes showing or not I'd put more soil over them for the winter. It'll insulate them better and keep moisture on them at least a bit while they're dormant. If you're not sure this advice is applicable please share some photos so we can get a better idea of the situation!