Farwell is a city in and the county seat of Parmer County, Texas, United States. Its population was 1,425 at the 2020 census. The city is locat…Farwell is a city in and the county seat of Parmer County, Texas, United States. Its population was 1,425 at the 2020 census. The city is located on the Texas-New Mexico border with the city of Texico, New Mexico across the border.