Ruling on one who kills another in self-defence and dies – does he have to pay blood-money or offer expiation?
Question

My father died and he had killed someone in self defence, and the family of the one who was killed had accepted the diyah (blood money). What is the expiation? Please note that he did not fast for two months or free a slave or feed the poor, and he had children. What is required of them?.
Praise be to Allah.The Muslim is obliged to defend himself and his family from any aggressor. He should ward him off with the slightest means, but if the assailant cannot be warded off except by killing, then it is permissible for the one who is being attacked to kill him, and he is not subject to retaliation (qisaas) and he does not have to pay any blood money (diyah) or offer any expiation (kafaarah), because sharee’ah has given him permission to kill in this case, and the slain aggressor is threatened with Hell, whereas the victim of aggression, if he is killed, is a martyr (shaheed) in sha Allaah. It makes no difference whether the aggressor is a Muslim or a kaafir. 
It was narrated that Abu Hurayrah (may Allaah be pleased with him) said: A man came to the Messenger of Allaah (peace and blessings of Allaah be upon him) and said: O Messenger of Allaah, what do you think if a man comes wanting to take my property? He said: “Do not give him your property.”  He said: What if he fights me? He said: “Fight him.” He said: What if he kills me? He said: “Then you will be a martyr.” He said: What if I kill him? He said: “He will be in Hell.” Narrated by Muslim (140). 
It was narrated that Sa’eed ibn Zayd (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “The one who is killed defending his wealth is a martyr, the one who is killed defending his family is a martyr, the one who is killed defending his religion is a martyr, and the one who is killed defending his life is a martyr.” Narrated by al-Tirmidhi (1421), al-Nasaa’i (4095), Abu Dawood (4772); classed as saheeh by al-Albaani in Irwa’ al-Ghaleel (708). 
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: 
The Sunnah and scholarly consensus are agreed that if a Muslim assailant cannot be warded off except by killing him, then he may be killed, even if the wealth that he wants to take is a small amount, as the Prophet (peace and blessings of Allaah be upon him) said in the saheeh hadeeth: “The one who is killed defending his wealth is a martyr, the one who is killed defending his life is a martyr, and the one who is killed defending his womenfolk is a martyr…” Fighting off an assailant is established in the Sunnah and by scholarly consensus. End quote. 
Majmoo’ al-Fataawa (28/540, 541). 
In al-Rawd al-Murabbi’ (p. 677) it says: 
If a person or one of his womenfolk, such as his mother, daughter, sister or wife, is attacked, or his property, whether a slave or an animal, is attacked, then he has the right to defend that by the least means that he thinks will ward off the attack. If he is able to ward it off with the least means then it is haraam for him to do more than that because there is no need for it. 
If he cannot ward off the attacker except by killing him, then he may do that, i.e., kill the assailant, and he is not liable for that, because he killed him to ward off his evil. End quote. 
Shaykh Saalih al-Fawzaan (may Allaah preserve him) said: 
The one who is attacked by someone who wants to kill him or attack his womenfolk such as his mother, daughter, sister or wife and violate their honour, or is attacked by someone who wants to take or destroy his property, has the right to defend himself against that, whether the attacker is a human or an animal. He should ward it off with the least that he thinks most likely will be able to ward it off, because if he is not allowed to defend himself that will lead to destruction and harm against himself or his womenfolk or his wealth, and because if he did not do that, people would overpower one another. If he cannot ward off the assailant except by killing him, then he has the right to do that, and he is not liable, because he killed him in order to ward off his evil. If the victim is killed then he is a martyr because the Prophet (peace and blessings of Allaah be upon him) said: “If a person’s wealth is sought unlawfully and he fights and is killed, then he is a martyr.” Narrated by Muslim and others from Abu Hurayrah (may Allaah be pleased with him). And he said:  A man came and said: O Messenger of Allaah, what do you think if a man comes wanting to take my property? … and he narrated the hadeeth quoted above. 
Al-Mulakhkhas al-Fiqhi (2/443). 
The person who is attacked should not hasten to kill the assailant until after he has exhausted other means of warding him off, such as reminding him of Allaah, scaring him and threatening him, seeking help from other people, or seeking the help of the police. But he may hasten to kill him if he fears that the aggressor is about to kill him. 
It was narrated from Qaboos ibn Mukhaariq that his father said: A man came to the Messenger of Allaah (peace and blessings of Allaah be upon him) and said: What if a man comes to me wanting to take my wealth? He said: “Remind him of Allaah.” He said: What if he pays no heed? He said: “Seek help against him from those who are around you of the Muslims.” He said: What if there are no Muslims around me? He said: “Then seek help against him from the ruler.” He said: What if the ruler is faraway from me? He said: Then fight him to defend your wealth, until you become one of the martyrs in the Hereafter or you protect your wealth.” Narrated by al-Nasaa’i (4081) and classed as saheeh by al-Albaani in Saheeh al-Nasaa’i. 
Secondly: 
This applies if it is proven that he killed him in self-defence with evidence such as the testimony of witnesses, or if the heirs of the slain person believe that he killed him in self-defence, or if there is strong circumstantial evidence to indicate that, such as if the slain person was known for evil and corruption, and he threatened to kill him – for example – in front of other people and so on. 
Shaykh Muhammad ibn Ibraaheem (may Allaah have mercy on him) said: 
If this person admits to killing him and claims that he did it in self-defence but the heir of the slain person does not believe him, then qisaas (retaliation) must be carried out. It says in al-Insaaf: this is our view, and the view of our companions. But if the slain person was known for aggression and evildoing, and there is circumstantial evidence that points to what the killer is saying, then it says in al-Insaaf: it says in al-Furoo’: No qisaas is required if he is known for evildoing. I say: This is the correct view, and circumstantial evidence should be taken into account. End quote. 
Majmoo’ Fataawa Ibn Ibraaheem (11/255, 256) 
Based on that, if your father killed this man in self-defence, then he does not have to do anything, whether that is offering expiation or paying blood money. 
And Allaah knows best.