The Quran

وَلا تَقتُلُوا النَّفسَ الَّتي حَرَّمَ اللَّهُ إِلّا بِالحَقِّ ۗ وَمَن قُتِلَ مَظلومًا فَقَد جَعَلنا لِوَلِيِّهِ سُلطانًا فَلا يُسرِف فِي القَتلِ ۖ إِنَّهُ كانَ مَنصورًا

Muhammad Asad

And do not take any human being's life - [the life] which God has willed to be, sacred - otherwise than in [the pursuit of] justice.¹ Hence, if anyone has been slain wrongfully, We have empowered the defender of his rights [to exact a just retribution] ;² but even so, let him not exceed the bounds of equity in [retributive] killing.³ [And as for him who has been slain wrongfully -] behold, he is indeed succoured [by God]!⁴

I.e., in the execution of a legal sentence or in a just war (see 2:190 and the corresponding note 167), or in individual; legitimate self-defence.
This refers to the legal punishment for homicide, termed qisas ("just retribution") and explained in 2:178 and the corresponding notes. In the present context, the term wall ("protector" or "defender of [one's] rights") is usually taken to mean the heir or next of kin of the victim; Zamakhshari, however, observes that it may also apply to the government (as-sultan): an interpretation which is obviously based on the concept of the government as the "protector" or "defender of the rights" of all its citizens. As regards the expression qutila mazlaman ("slain wrongfully"), it is obvious that it refers only to cases of wilful homicide, since the concept of zulm applies in the Qur'an exclusively to intentional and never to accidental wrongdoing.
Thus, the defender of the victim's rights (in this case, a court of justice) is not only not entitled to impose a capital sentence on any but the actual murderer or murderers, but may also, if the case warrants it, concede mitigating circumstances and refrain from capital punishment altogether.
I.e., he is avenged in this world by the retribution exacted from his murderer, and in the life to come, blessed by the special grace which God bestows on all who have been slain without any legal or moral justification (Razi). Some of the commentators, however, relate the pronoun "he" to the defender of the victim's rights, respectively, to the latter's heir or next of kin, and explain the above phrase as meaning "he is sufficiently helped by the law of just retribution (qisas) and should not, therefore, demand any punishment in excess of what is equitable".