As said earlier in the comments you are confusing things neither would an unmarried Muslim woman get half of the punishment of a married one. As there's no half death punishment, actually this is the argument some quranists put in to "prove" that the punishment by stoning to death doesn't exist and has no backup in the qur'an. As the only quoted punishment is that of 100 lashes.
Secondly slavery is something which clearly plays a role in shar'ia, is quoted in the qur'an and fills chapters of books of fiqh about specific rulings for slaves. Therefore one could have a Muslim slave (explanation see later), but this doesn't mean that one could make a Muslim a slave as this is haram.
Verse 4:25 first speaks about marriage for a (Muslim) man who cannot afford marrying a free woman and is no more able to wait until he has the means for such a marriage. It explains to him that marrying a believing (female) slave (of another man) is allowed. It actually uses the wording:
believing women
Ibn Kathir here says:
(They may wed believing girls from among those whom your right hands possess,) meaning, they are allowed to wed believing slave girls owned by the believers.
This actually means that it is allowed for him to marry a salve of another man. But this slave must be counted among the believing ummahs: a Muslim, and maybe a Christian or Jew in first place, all these have revelation about tawheed and are known as people of the book.
Some scholars therefore even say that a concubine of a man can only be from among those.
However a large majority of scholars say that the words "believing women" excludes Jews and Christians according to imam al-Qurtobti and al-Mawsu'a al-Fiqhiya even excludes the permission for marrying them.
This is because a man should chose a good wife (and mother for his children) and a believing woman is better than one from among the people of the book and a free and faithful one is certainly better than a slave girl that another man owns (as if both would have offspring the children would be slaves of the slave girl owner which is rather disliked).
The verse also makes clear that for marrying a slave girl the agreement of the slave owner is necessary and that they will receive the mahr (not their owners):
So marry them with the permission of their people and give them their due compensation according to what is acceptable.
Such a marriage is permissible, but certainly disliked therefore the conditions for it are clearly mentioned. Because it would be much better to marry a free woman than a slave or freeing a slave and marrying her. Scholars say if a man doesn't have the means for marrying a free Muslim lady and could afford marrying either a faithful slave girl of another man or a woman from among people of the Book the later would be the better choice.
Note that making a Muslim a slave is haram, but a slave could convert to Islam in Muslim a household or a Muslim could be enslaved by non-Muslims however this case I would exclude for further discussions here. As I doubt that this actually would go along with the meaning of this verse.
But the verse further also shows the punishment for this married slave girl (or woman) in case she commits zina then only half the punishment of a free non-married Muslim girl (woman) would apply saying:
... if they should commit adultery, then for them is half the punishment for free [unmarried] women.
While the agreed upon punishment for a free non-married Muslim woman is explained in surat an-Nur:
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. (24:2)
So therefore she would receive fifty lashes instead of hundred.
The sunnah even ordered punishment for non married slave girls:
O people, impose the prescribed punishment upon your slaves, those who are married and those not married, for a slave-woman belonging to Allah's Messenger (ﷺ) had committed adultery, and he committed me to flog her. But she had recently given birth to a child and I was afraid that if I flogged her I might kill her. So I mentioned that to Allah's Apostle (ﷺ) and he said: You have done well. (Sahih Muslim).
In Fiqh slavery is treated somehow like a financial contract. Therefore if two slaves have offspring this could be benifcal for the slave owner. While if he is the father of the children his concubine would have certain advantages compared to other slaves, as once he'd die she would be free and the child would be his child. But the case discussed in the verse would create a conflict between the parties which is the reason why these kinds of marriages are disliked. Slaves basically don't have the right to deny or reject their owners orders or wishes, but they could have contracts with him or others.
I've pointed at this in my answer on sex slaves. From this perspective the punishment and its severity makes also sense, as a slave has certain limitations in his/her practice and freedom he/she shouldn't get the same punishment as a free person and of course the interest of the owner must be taken into account a dead slave is rather a unuseful one as hard as it might sound for us today.
