I got some pictures and did some research.
Wood sorrel (Oxalis stricta) is this stuff in the first two pictures that's around here. It's tangy and tasty and we ate it as kids but this isn't what we called sourgrass, although some people call it that. The seed heads, shaped like okra pods, pop open when they're ready, scattering out the sticky little seeds. It grows well in part shade, I'm weeding it out all the time in the garden, it loves being under other things. I've never come across tubers but I'll investigate more. Research is preliminary but I didn't find any reference yet to edible tubers with Wood Sorrel (Oxalis stricta). ("They may form colonies arising from slender but tough underground stems (rhizomes), but more often are individual, seed-grown plants."
https://hort.extension.wisc.edu/articles/common-yellow-woodsorrel-oxalis-stricta/ )
https://plants.ces.ncsu.edu/plants/oxalis-stricta/
View attachment 2867070
View attachment 2867068
I also found what we used to call sourgrass as kids, and someone told me years ago this was sorrel. This below is called Red Sorrel, or Common Sheep Sorrel (Rumes acetosella). It has tall thin spiky red-flower stems. It is not in the oxalis group but does have oxalic acid in it. The arrow-shaped leaves are very tasty. Larger cultivated kinds are made into sorrel soup. The only ones I could find today are growing on big gravel, making it hard to dig, but I'll keep looking.
It has "creeping rhizome roots"
https://plants.ces.ncsu.edu/plants/rumex-acetosella/.
https://www.fs.fed.us/database/feis/plants/forb/rumace/all.html
What the chickens found were individual tubers/bulbs, not rhizomes on roots.
View attachment 2867078
I am doubting that what the chickens were eating is either of these. But I don't really know. Best to try to find and grow some tubers like
@rural mouse? or
@fuentemoon? suggested!