Wa Alaykum Salam. There are 2 opinions about this issue:
- Recm (stoning to death) is not mentioned in Quran. Therefore there should be no killing. The punishment should be given according to Quran.
- There are hadiths about recm. Usually (maybe in all) the ones that was killed was all married ones. There is also a claim that there were verses about recm, but they are eaten by a goat. This claim is also based on a hadith.
In history, adultery is punished by 2 ways. If the committed one is a single, Quranic verses are considered. If the committed one is married, then recm is considered. But there are not much this issue in history, because the requirements about it are very strict. Here are 3 of them:
- There should be 4 witnesses.
- 4 of them should see simultaneously.
- They should see very clearly (as sword inside its scabbard). (They were under quilt isn't work)
According to my belief, Quran has never been changed (it is just as Mohammad(puh) as transfered). So, if Quran talks clear about something, I believe it, I don't consider hadiths. Because they may be made up.
And the two who commit it among you, dishonor them both. But if they repent and correct themselves, leave them alone. Indeed, Allah is ever Accepting of repentance and Merciful. (Surat An-Nisā' 4/16)
How can you expect repentance from a dead one?
And whoever among you cannot [find] the means to marry free, believing women, then [he may marry] from those whom your right hands possess of believing slave girls. And Allah is most knowing about your faith. You [believers] are of one another. So marry them with the permission of their people and give them their due compensation according to what is acceptable. [They should be] chaste, neither [of] those who commit unlawful intercourse randomly nor those who take [secret] lovers. But once they are sheltered in marriage, if they should commit adultery, then for them is half the punishment for free [unmarried] women. This [allowance] is for him among you who fears sin, but to be patient is better for you. And Allah is Forgiving and Merciful. (Surat An-Nisā' 4/25)
What is the half of the punishment of death?
The [unmarried] woman or [unmarried] man found guilty of sexual intercourse - lash each one of them with a hundred lashes, and do not be taken by pity for them in the religion of Allah , if you should believe in Allah and the Last Day. And let a group of the believers witness their punishment.
The fornicator does not marry except a [female] fornicator or polytheist, and none marries her except a fornicator or a polytheist, and that has been made unlawful to the believers. (Surat An-Nūr 24/2-3)
I don't know where is this [unmarried] comes from. In all of other translations, it doesn't exist. You can look by clicking the link and selecting other translations from the left menu. Also, 24:3 mentions about the marriage of a fornicator. How can a dead marry? You may claim this punishment is only those who are single, but there is something called divorce.
I believe these are all verses about the punishment of adultery. I looked from a Quran index about adultery and filtered the ones about punishment. As you see, there is no mention about death. Only 3 things are said:
- Lash punishment for each
- Not - marrying with them
- Dishonor them