LITTLE MOUNTAIN, S.C. — Wanted: a mayor for this tiny South Carolina town.

Like many rural communities across the country, Little Mountain has seen its population drop over the decades. Businesses closed on Main Street. Residents moved to nearby Columbia, seeking jobs and a faster pace.

Now the one-stoplight town, population 292, faces a more existential threat to its future: Nobody wants to be the mayor. No candidates ran in an election to replace the retiring mayor in November and, more unusual, the top two write-in recipients declined the job.

“We have not found anyone for the job yet,” said Melvin Bowers, a town councilman.

It is not unheard-of for offices to go unfilled in small electorates. In Mount Sterling, Iowa, after none of the 44 residents ran for City Council or mayor last year, the 105-year-old city disbanded. In Lynchburg, S.C., in 2010, a write-in candidate for mayor was reluctantly sworn in.