Just sounds like a rural town to me. Whole police departments have been disbanded due to funding, corruption, and public outcry. Services are (often poorly) handled by county or neighboring towns temporarily or even permanently.

Here’s a recent one in Alabama, same Sheriff situation as OP. https://www.vice.com/en/article/m7ggmn/vincent-alabama-polic...

> The city will now rely on a neighboring sheriff’s office in Shelby County to answer emergency calls.