I don't know anything about the townpersonally, but I can provide you with some facts I found about it:
Tompkinsville is a city in Monroe County, Kentucky, United States. The population was 2,660 at the 2000 census. It is the county seat of Monroe County. As of the censusGR2 of 2000, there were 2,660 people, 1,169 households, and 702 families residing in the city. The median income for a household in the city was $18,267, and the median income for a family was $23,361. Males had a median income of $21,587 versus $16,541 for females. The per capita income for the city was $15,975. About 24.5% of families and 29.0% of the population were below the poverty line, including 35.8% of those under age 18 and 23.9% of those age 65 or over.
Based on those statistics and the small population, I would venture to say that your prediction on job availability would be correct. Often times, small kentucky towns like Tompkinsville are only kept afloat by a few small family businesses or by a factory that moves into the town.
Sorry I can't be more help and good luck in your search.