Answer: Strongyloides stercoralis infection.
Seen here are numerous rhabditiform S. stercoralis larvae, some possible filariform larvae, and embryonated eggs with viable larvae within. This level of infection is consistent with Strongyloides hyperinfection and warrants a rapid call to the clinical team to alert them to the diagnosis.
There were a lot of great comments on this case. Florida Fan, Angelica Maria and Khalid Elfeel nicely discussed the presence of the short buccal cavity and genital primordium - keys feature for differentiating the rhabditiform (L1) larvae of S. stercoralis from the similar-appearing larvae of the hookworm. Shown below is a comparison of the buccal canals of Strongyloides and hookworm rhabditiform larvae (latter courtesy of the CDC DPDx).
Here is an another composite image of the readily-identifiable genital primordium in S. stercoralis rhabditiform larvae (the one in hookworm rhabditiform larvae is inconspicuous).
I should mention that the hookworm larvae come into the differential only when unfixed stool is allowed to sit for more than a day before being examined, thus allowing time for the eggs to mature and hatch. Only unembryonated hookworm eggs are seen in freshly-passed stool, and it takes 1-2 days for the eggs to mature and hatch.
In comparison, seeing S. stercoralis eggs in stool is quite unusual. This is because eggs of S. stercoralis are usually laid in the intestine and quickly hatch to release rhabditiform larvae. Florida Fan, Mark Fox and Sugar Magnolia raised the possibility that the presence of eggs indicates a very high level of infection, which I believe to be correct in this case.
Finally, Anon reminded us that Kentucky is endemic for strongyloidiasis and therefore something that should be considered in patients from this area - especially before starting any immunosuppressive therapy. Along these same lines, you may be interested to see this recent article of hookworm in the American south, published in The American Journal of Tropical Medicine and Hygiene. There is an interesting associated news commentary that you can read HERE. It's so sad to see the poor sanitary and living conditions that are still present in the United States.