WASHINGTON — In June of 2010, four boys were playing in the dry bed of the Rio Grande that separates El Paso from Juárez, Mexico. The international borderline, unmarked, runs through the middle of the culvert.

The boys dared one another to run up a concrete incline and touch the barbed wire of the American border fence.

An American border guard, Jesus Mesa Jr., grabbed one of them. Another boy, Sergio Hernández Guereca, fled, and he made it back to Mexico before Mr. Mesa shot him in the head from about 60 feet away, killing him. Sergio was 15.

Last week, the Supreme Court agreed to decide whether Sergio’s parents may sue Mr. Mesa for violating the Constitution by using excessive force. If not, lawyers for the parents argue, then Sergio died in “a unique no-man’s land — a law-free zone in which U.S. agents can kill innocent civilians with impunity.”