The biblical justice system creates a unique bridge between formal criminal law and personal closure by placing the execution of an intentional murderer directly into the hands of the victim's closest relative. This relative acts as the avenger of blood. If the victim leaves behind no family, the court is obligated to appoint an avenger to carry out the sentence and ensure justice is served [ביאור שטיינזלץ, תורה תמימה, רש״ר הירש]. Executing the guilty party is not merely an option; it is a strict Commandment imposed on the avenger once the court has proven the murderer's guilt and issued a final sentence [רלב״ג]. Even if the relative apologizes and claims he is unable to take a life, the obligation stands, and he must pursue the murderer to fulfill the punishment [תורה תמימה]. Furthermore, the avenger is not restricted to specific weapons. The execution can be performed using any lethal means available, whether stone, wood, or iron [מלבי״ם].
The exact nature of the encounter between the avenger and the murderer is a subject of deep discussion, as the underlying language hints at something more complex than a simple chance meeting [אבן עזרא, הכתב והקבלה, נתינה לגר]. The primary approach among certain commentators is that this grants the avenger broad spatial authority. If an intentional murderer flees to a city of refuge without the court's permission, or if the justice system fails to punish him, the avenger is permitted to strike the murderer wherever their paths cross, even within the bounds of a city of refuge [רש״י, שפתי חכמים, מזרחי, משכיל לדוד, רש״ר הירש].
Conversely, another line of thought completely rejects the idea of a random street killing. According to this view, the law does not permit such a disregard for human dignity that a person would be struck down casually in public. Instead, the encounter refers to the formal execution of justice. Only after the court has officially sentenced the murderer do the judges hand him over—bound and helpless—to the avenger to carry out the punishment [שד״ל, הכתב והקבלה, אוהב גר]. Adding another layer to this event, some explain that the nature of the strike is rooted in the concepts of crime and spiritual blemish, meaning the avenger puts the murderer to death specifically because of the severe sin that has attached itself to him [נתינה לגר].