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
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.