The residents of Strafford, Vt., cannot imagine their town without Coburns’ General Store, a hub so quirky and cozy, so steeped in New England authenticity, it could be the setting for a novel — or the inspiration for a song.

In fact, the store and the community it serves loom large in the songs of Noah Kahan, the 27-year-old folk-pop sensation who recently became Strafford’s most famous son. Now, Mr. Kahan’s fans around the country and the world cannot imagine his hometown without Coburns’, either: They drop in often to soak up the rural vibes that shape his music, snapping selfies with the store’s owner, Melvin Coburn, 80.

But the fate of the general store, run by Mr. Coburn and his wife, Sue, for the past 47 years, is uncertain. The couple is past ready to retire, but since listing the property for sale two years ago, they have found no buyer. A small group of Strafford residents is trying to find a way to keep the business going; they recently established a nonprofit community trust and are well on their way to raising the $1.8 million needed to buy Coburns’ and set aside funds for its repair and upkeep.

Their next task is to recruit a new proprietor to lease and run the store, which has been in Strafford, in east central Vermont, since the 1880s. Coburns’ sells groceries, saving residents the 25-mile trip to the nearest large supermarket, and it also serves as an essential gathering spot for the town — a place to see neighbors, catch up on local news and strengthen the connections that are critical to rural life.