ELEPHANT BUTTE, N.M. — This is the story of a leash, a law and a city’s dueling definitions of compassion. It is a story of limits tested and stretched; of strife, threats and, possibly, compromise.

Mostly, though, it is a story about a dog named Blue who, this week, brought this small desert city together after nearly tearing it apart.

The City Council held a meeting on Wednesday to decide Blue’s fate. He was born here 11 years ago and was soon abandoned to wander the streets, even before Elephant Butte — sandwiched between a city named Truth or Consequences and a desert basin called the Jornada del Muerto, the route of a dead man — became a city. He has been no one’s dog, or everybody’s dog.

Blue’s thick fur is speckled with gray, a trademark of his breed — he is an Australian cattle dog — but also a sign of his age. His legs are too feeble to run; his walk is more like a plod. There was a time when he could dash across State Highway 195 to “do his business,” as one supporter put it, in a spot that he has used for as long as anyone can remember.