Answer
Wa`alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother in Islam, we really appreciate your question.
Admittedly, applying the hudud (i.e. prescribed penalties) on the culprits is a fundamental and indispensable matter, and halting them is a grave crime in the eyes of Allah. People should observe Islam as a complete entity and act upon its teachings and judgments in the whole spheres of their lives. It is sorrowful that most Muslim countries have refrained from the enforcement of the hudud of Islam.
However, neglecting the Islamic hudud by a government does not justify or legalize applying these penalties at the individual level. Rather, application of hudud is totally authorized to the ruler, not the individuals.
As regards your question, Dr. Salah Al-Sawi, secretary-general of the Assembly of Muslim Jurists in America (AMJA), stated,
The basic rule concerning Shari`ah punishments is that they are delegated to the imams (the legitimate rulers), since they have the means of thorough investigation, examination, and verification that would not be available to anyone else. Also, when the imams implement the Shari`ah punishments, it does not lead to confrontations and killings among people.
Therefore, if a man sees his sister committing zina, he does not have the right to kill her for two reasons:
1- The Shari`ah did not make death the only, unvarying punishment for zina. On the contrary, it differentiated between fornicators and adulterers; Almighty Allah made lashing and banishment the punishment for those who are unmarried, and stoning the punishment for those who are married.
2- Referring the application of the Shari`ah punishments to individuals would start a chain reaction of multiple harms: people killing one another, transgressing the limits, and sinking into the chaos of hostility and revenge. This should be perfectly clear to anyone who contemplates the issue.
Although the brother of such a woman does not have the right to execute her or inflict the divinely ordained criminal punishment on her for the above-mentioned reasons, he is still required to express disapproval of such an act. He must forbid her in any possible way from practicing zina again. The same would also apply to the guardian of a murder victim. Even if a state’s criminal law is not based on Islamic Shari`ah, a guardian does not have the right to execute the murderer, for the same reasons mentioned above.
In fact, this is particularly significant in the context of murder, due to the enormity of the crime of murder and the guardian’s desire to take revenge, with which the principles of justice may be ignored most of the time.
Indeed, we have seen the calamity and affliction brought by the custom of retaliation in the communities where it has spread. Perhaps in seeking judgment, reconciliation, and acceptance of blood money, or forgiveness, there is a way out, albeit temporarily, in situations like this. We should emphasize here that the way out of these problems is to comply with Shari`ah and implement the hudud ordained by Almighty Allah at the hands of the rulers, for establishing one of these hudud in a land is better for its people than if it were to rain every morning for 40 years.
Allah Almighty knows best.