Gemara

(Beraisa): If one stole an animal and gave it to another (a Shali'ach) to slaughter or sell it (and he did), the thief pays four or five.

Normally, Ein Shali'ach l'Devar Aveirah. This is an exception.

Question: What is the reason?

71a - Answer #1 (Rava): "And he slaughtered it or sold it" - just like selling is through another, also Shechitah (one is liable through another).

Answer #2 (Beraisa - Tana d'Vei R. Yishmael): "(Slaughter) or (sell)" includes through a Shali'ach;

Answer #3 (d'Vei Chizkiyah): "Tachas (in place of)" includes through a Shali'ach.

Kidushin 42b (Beraisa): If Reuven sent Shimon to buy something, and he gave to him Hekdesh money, if he fulfilled his mission, Reuven transgressed Me'ilah.

Normally, Ein Shali'ach l'Devar Aveirah. A Gezeirah Shavah "Chet-Chet" teaches that just like one can make a Shali'ach for Terumah, also for Me'ilah.

Question: Why don't we learn from Me'ilah to other Aveiros?

Answer #1: Me'ilah and Shlichus Yad are Shenei Kesuvim, therefore, we do not learn to other cases.

Answer #2: According to Beis Shamai (who disagree about Shelichus Yad), Me'ilah and selling or slaughtering a stolen animal are Shenei Kesuvim.

Answer #3: According to the opinion that that Shenei Kesuvim teach to other places, Beis Shamai learn from Shechutei Chutz (slaughtering Kodshim outside the Mikdash), it says "to that man", not to his Shali'ach. (An extra verse teaches that we learn to all other Aveiros!)

Rishonim

The Rif and Rosh (Bava Kama 28a and 7:6) bring the Gemara on 79a.

Rosh: He is exempt on Shabbos even through a Shali'ach, for the Shechitah does not permit (the meat, for it came through Melachah on Shabbos).

Rif and Rosh (Bava Kama 29a and 7:9): In the entire Torah, Ein Shali'ach l'Devar Aveirah, except for a thief who made a Shali'ach to sell or slaughter.

Rambam (Hilchos Geneivah 2:10): If Levi (a thief) gave the animal to Ploni to slaughter or sell it, and Ploni did so, the thief pays four or five.

Rambam (3:6): If Levi gave the animal to Ploni to slaughter it, and Ploni did so on Shabbos, Levi pays four or five, for Levi is not Chayav Misas Beis Din.

Rambam (Hilchos Me'ilah 7:2): If Levi told David to eat meat, and it was of an Olah, only David transgressed Me'ilah, for there was another Isur in addition to Me'ilah. In the entire Torah, Ein Shali'ach l'Devar Aveirah, except for Me'ilah with no other Isur involved.

Maharit (Kidushin 42b (on Rif) DH ul'Devar): Yesh Shali'ach l'Devar Aveirah also regarding Shechitah and selling, and Shlichus Yad! If a Shomer told someone to be Shole'ach Yad, the Rambam obligates the Shomer for negligence, not due to Shelichus. A thief who told another to slaughter or sell is punished for benefit, even without Shelichus. This is called Shenei Kesuvim, for if we could learn from Me'ilah, we would not need verses for Shlichus Yad or Shechitah. Beis Hillel use the Drashah to obligate for Shechitah or selling via one who cannot be a Shali'ach. Beis Shamai use it for Shenei Kesuvim, and obligate only via a Shali'ach. Perhaps we conclude that they obligate via anyone, and learn Ein Shali'ach from Shechutei Chutz.

Note: Seemingly, the Safek about one who cannot be a Shali'ach applies also to Beis Hillel, according to the opinion that learns from Shenei Kesuvim.

Poskim

Tur (CM 350:18): If Levi gave a stolen animal to Ploni to slaughter it on Shabbos, and Ploni did so, the Rambam obligates four or five, for Levi is not Chayav Misas Beis Din. The Rosh exempts, for one may not eat from the slaughter

Rebuttal (Mishneh l'Melech Hilchos Geneivah 3:6): If Levi commanded him to slaughter on Shabbos, also the Rambam exempts from four or five. Normally, Ein Shali'ach l'Devar Aveirah. The Chidush that Yesh Shali'ach for Shechitah and selling is only when no other Isur is involved, like the Rambam says in Hilchos Me'ilah. Surely, Ein Shali'ach to slaughter on Shabbos, therefore the Shelichus is Batel also for four or five. The Tur holds that the Rambam was imprecise. Really, Levi is liable even if he commanded Ploni to slaughter on Shabbos. The Rambam in Me'ilah refutes this.

Sha'ar ha'Melech (Hilchos Geneivah 5:6): Tosfos (Bava Kama 71a DH bi'Shomo) obligates a thief who authorized a Shali'ach to slaughter 'even for idolatry, if you want.' It seems that had he commanded him to slaughter for idolatry, he would be exempt. However, there is no proof from the Rambam in Me'ilah. There, the Shelichus (to eat an Olah) necessarily entails an Aveirah other than Me'ilah, and Ein Shali'ach to eat an Olah). Here, he could slaughter without Chilul Shabbos!

Defense (Hafla'ah Kesuvos 33b DH v'Chi and Ketzos ha'Choshen 232:1 DH uv'Tur): Shechitah is unlike Me'ilah, in which Shelichus is needed. Here, the thief is liable for benefit. R. Yochanan and Reish Lakish (Bava Kama 68b) obligate a thief who sold before despair, even though the sale is void. Here also, even though the Shelichus is Batel due to Ein Shali'ach, the thief is liable. The same applies to commanding a Shali'ach to slaughter to idolatry.

Question (Pnei Yehoshua): According to those who are stringent to say that Yesh Shelichus l'Nochri, why is telling a Nochri to do Melachah on Shabbos only mid'Rabanan? Since the Nochri is not Bar Chiyuva, Yesh Shali'ach l'Devar Aveirah, so the Meshale'ach transgresses mid'Oraisa!

Answer (Beis Meir EH Sof Siman 5): Shabbos is like a Mitzvah on a person's body, that he rest on Shabbos. Shelichus does not apply, just like one cannot make a Shali'ach to wear Tzitzis (Tosfos Rid Kidushin 42b DH Sheani). Therefore, a command to slaughter on Shabbos does not Mevatel Shelichus.

Beis She'arim (OC 76): Even if he commanded to slaughter on Shabbos, this could be without an Isur of Shabbos, e.g. for a sick person.