There's jobs in the local area. At 50 miles nebraska.gov Jobs has ~2,500 [1], Indeed has ~1,000 [2], and ZipRecruiter has ~500 [3]. However, not many that a Tyson Food cattle worker can probably easily qualify for. Most tend to be at least somewhat specialized, and quite a few that require something like nursing, healthcare, education, or otherwise.
American Foods Group LLC in Kearney, NE apparently at least has jobs that are related "Beef Production, $19.65 - $26.00, 4500 employees, process 4 million pounds of beef a day". [4] Looks like maybe the best available in the area.
Still, even if several thousand leave, that's still a pretty enormous hit on 11,000. Lose a 1/4 - 1/2 your population in a couple months or so.
[1] https://neworks.nebraska.gov/vosnet/jobbanks/joblist.aspx?en...
[2] https://www.indeed.com/jobs?q=&l=Lexington%2C+NE&radius=50&s...
[3] https://www.ziprecruiter.com/jobs-search?search=&location=Le...
[4] https://www.indeed.com/viewjob?jk=30014a5bd9219934&from=shar...