It appears that one of the small border communities affected by current fence plans may be Columbus, New Mexico
Columbus is a small community of ~1600 people three miles north of the border. On the Mexican side of the border is Puerto Palomas with ~4600 people, so this is a smaller community than many on the border. It is also relatively isolated between El Paso and Antelope Wells.
The town website talks about living life on the borderline
Columbus, New Mexico is an American Historical Gem. Bordering Palomas, Mexico and rich with history. Columbus is best known as the village raided by the famous Pancho Villa in 1916. Interestingly that raid was the first time a foreign army invaded the continental United States and killed U.S. citizens prior to the World trade center…
Shortly after Trump took office, a story was written about Columbus. There was three miles of pedestrian fencing. Otherwise residents noted Columbus as a fairly quiet section and were at least as concerned about economic effects as any border crossing.
Columbus is also a place where border fencing was accidentally built in Mexico and had to be redone.