Kerisos, Chapter 2, Mishnah 5. Our Mishnah comes to define what a "shifchah charufah" is and what case it is talking about. As was mentioned in passing, the halachah deals with a woman who is half a Canaanite maidservant and half a regular Jewish girl. How is such a situation possible?
How a situation of half maidservant and half free woman is created:
A woman was initially owned by two Jews as a full Canaanite maidservant. One of the two freed his portion, and from now on she is half a free woman and half a maidservant.
To whom is such a woman fit to be bound?
If she were a full Canaanite maidservant - she could be paired with a Canaanite slave, meaning a regular non-Jewish slave.
If she were a free woman - she could marry a regular Jewish man.
However, a regular Jewish man cannot marry a Canaanite maidservant, and a free Jewish woman cannot marry a Canaanite slave. Therefore, her Jewish half cannot be bound to a Canaanite slave, and her maidservant half cannot be bound to a regular Jewish man, and she is left without a match.
There is one person who has the ability to be bound to her: the Hebrew slave. The Hebrew slave is a full Jew in every respect - he is sold because of his debts and serves his Jewish master for six years, and all the mitzvos apply to him. However, an exceptional law was introduced regarding him: under certain circumstances, he is permitted to be bound to a Canaanite maidservant. Because of this, he can be bound to both a regular Jewish woman and a Canaanite maidservant, and therefore he is the only one fit for this woman who is half maidservant and half free woman.
However, this is not a marriage in the regular sense, since the half of her that is a Canaanite maidservant is not subject to kiddushin, whereas her other half is.
The language of the verse:
The Torah says: "And if a man lies with a woman... and she is a maidservant designated for a man." The word "necherefes" is unusual, and Rashi notes that this is a unique word meaning designated or bound. We cannot say "married", since kiddushin does not take hold on her, but rather she is bound to a man. The verse continues: "vehofdeh lo nifdasah" - and in literal translation: redeemed and not redeemed. Therefore, one who lies with such a woman, who is partially married, "designated" to a man, is not subject to the death penalty, because she was not freed.
Two inferences arise from the verse, and the Mishnah deals with them:
The verse says "vehofdeh lo nifdasah", as if stating a contradiction. Was she redeemed or was she not redeemed?
The verse repeatedly emphasizes that she was not redeemed and is not a free woman, and this repetition requires an explanation.
The three opinions in the Mishnah:
First Opinion: The Mishnah asks for the definition of the maidservant for whom a man incurs liability for the guilt offering of a designated maidservant, and answers that this refers to a woman who is half free and half maidservant, as described above. And from where do we know this? From the verse "vehopdeh lo nifdatah" - redeemed she was not redeemed, meaning yes and no, since she is half one way and half the other.
Rabbi Yishmael disagrees and says that the maidservant we are dealing with, for whom one who sleeps with her is liable for this special guilt offering, is a completely ordinary Canaanite maidservant, who is not Jewish at all, and who is designated for a Canaanite slave. His reasoning: Rabbi Yishmael's approach is that "the Torah speaks in the language of men," and one should not expound a lesson from a doubled expression. The intent of the verse is that she certainly was not redeemed, and she is fully owned by her master, as it is the way of the Torah to express itself in this manner. Therefore, nothing can be learned from the wording "freed, not freed," and we have already found similar instances elsewhere.
Rabbi Elazar ben Azaryah replies to Rabbi Yishmael: Indeed, as a rule, the Torah speaks in the language of men and we do not expound doubled expressions, but in this verse, there is a necessity to expound, since it concludes by stating that she was not a free woman. Why would the verse bother to mention this? After all, all the other forbidden relations apply to free women. And if it was already said that she is not a free woman, why does the verse repeat it a second time? Perforce, in this case, there is something to expound: that she is half freed and not completely freed.
In his words: All the other forbidden relations are stated regarding free women, ordinary free women and not maidservants. Since the Torah took the trouble to say that in this case she was not freed even though she is considered a forbidden relation, what is left for it to exclude? Necessarily, this exceptional case, where she is half freed and half redeemed. For this reason, the Torah needed to repeat and say that this young woman was not completely freed, and therefore one who is with her in this unusual situation is liable for a guilt offering.
In summary: As stated above, the halachah follows Rabbi Akiva, and essentially Rabbi Elazar ben Azaryah - that we are dealing with someone who is half free and half maidservant, a woman whose status was created through the freeing by one of her two owners, and who is fit to be bound only to a Hebrew slave. And from the repetition "vehopdeh lo nifdatah" - redeemed she was not redeemed, we learn the special law of a designated maidservant.