Is it permissible to kill a thief who attempted to rape his wife, stripped her of her clothes, and kissed her, knowing that the husband identified the perpetrator?

This person's act is a heinous crime deserving severe disciplinary punishment (ta'zir), but it is not permissible to kill him because taking a life is one of the gravest major sins. Allah Almighty says: "And whoever kills a believer intentionally, his recompense is Hell, wherein he will abide eternally, and Allah has become angry with him and has cursed him and has prepared for him a great punishment." And the Prophet, peace and blessings be upon him, said: "A person remains within the scope of his religion as long as he does not shed unlawful blood." Moreover, his action does not necessitate killing, and killing him would corrupt your religion and your worldly life and expose you to punishment. You must take official measures to punish him and leave the matter to the judiciary, and undertake to protect and look after your family.