Gemara

39b: According to Abaye, R. Yakov holds like R. Yehudah, that when an animal becomes Mu'ad, it retains liability to pay half-damage like a Tam.

40a (Ravina): Rava agrees about this.

45b (Mishnah - R. Meir): If Reuven tied his animal with a Mosirah (a rope around its neck), or locked (a gate) in front of it properly, and it escaped and damaged, he is liable, whether it is Tam or Mu'ad;

R. Yehudah says, a Tam is liable, and a Mu'ad is exempt. It says "if he will not guard it", and this is guarded!

R. Elazar says, a Mu'ad cannot be guarded. It must be killed.

R. Meir holds that people normally do not guard their oxen. The Torah obligates a Tam to pay; this mandates a minimal guarding. "If he will not guard it" obligates proper guarding for a Mu'ad. A Gezeirah Shavah teaches from a Mu'ad to a Tam.

R. Yehudah holds that people normally guard their oxen (minimally). The Torah obligates a Tam to pay; this mandates a proper guarding. "If he will not guard it" is a second verse mandating a proper guarding, so it excludes. I.e., a minimal guarding suffices for a Mu'ad. "If he will not guard it" limits this law to a Mu'ad.

(Beraisa - R. Eliezer ben Yakov): A minimal guarding suffices for Tam and Mu'ad.

He learns that a minimal guarding suffices for a Mu'ad, like R. Yehudah. He learns Tam from Mu'ad from the Gezeirah Shavah, like R. Meir.

(Rav Ada bar Ahavah): R. Yehudah holds that a minimal guarding exempts only the extra payment of a Mu'ad, but not half-damage that a Tam pays.

(Rav): An ox Mu'ad to gore with the right horn is not Mu'ad for the left horn.

Question: Rav cannot hold like R. Meir, who requires a proper guarding for Tam and Mu'ad. If he holds like R. Yehudah, he could have taught about the two sides of the right horn itself (a minimal guarding exempts only its Mu'ad side)!

Answer: Really, he holds like R. Yehudah. Rav disagrees with Rav Ada. Rav holds that only in this case R. Yehudah holds that a Mu'ad has a Tam side.

(Abaye): R. Elazar (who said that a Mu'ad must be killed) holds like R. Noson;

(Beraisa - R. Noson): "Do not put blood in your house" forbids raising a wild dog or erecting a rickety ladder in one's house.

55b: A minimal guarding suffices for Shen and Regel.

Support (Rabah): The above Mishnayos discussed an ox. Our Mishnah switched to 'flock' (they damage through Shen and Regel, but do not gore). A minimal guarding suffices for them, even though they are Mu'ad from the beginning.

Rishonim

Rif: R. Elazar obligates b'Yedei Shamayim for not slaughtering a Mu'ad. Even though the Halachah follows R. Noson, the Halachah does not follow R. Elazar.

Rambam (Hilchos Nizkei Mamon 7:1): If Reuven tied his animal with a Mosirah, or locked (a gate) in front of it properly, and it escaped and damaged, if it is Tam it pays half-damage. If it is Mu'ad, he is exempt, for it says "if he will not guard it." This was guarded, so he is exempt. The same applies if it did damage for which it is Mu'ad from the beginning, e.g. it ate things that it normally eats, or broke with its foot while walking normally.

Rambam (2): If it was Mu'ad only for the right horn, and it was guarded properly and left and damaged, it pays half for goring with either horn.

Ra'avad: It pays half only mi'Gufo (from the animal itself).

Question (Shiltei ha'Giborim 20a:1): Tosfos explains that all laws of Tam still apply to the Tam half, e.g. mi'Gufo. However, admission does not exempt it. After testimony made it Mu'ad, half-damage is not a fine. The Rambam contradicts what he wrote in Halachah 1, that a proper guarding totally exempts a Mu'ad!

Answer (Lechem Mishneh and Gra in Frankel Rambam): The Rambam explains that Rav teaches that we say that the Tam side is intact (like Rav Ada taught) only for such an animal that is not totally Mu'ad.

Rosh (4:6): The Halachah follows R. Yehudah. Even though some texts say 'R. Yehudah holds that Stam animals are not considered guarded', R. Yehudah holds that half-damage is a fine. Even though the owner does not consider them to be guarded, and he guards them, they do not normally damage, especially when they are guarded. A minimal guarding suffices only for the Mu'ad side, but the Tam side is liable, like Rav Ada. Even though Rav disagrees, the Halachah follows Rav Ada, for on 39b, the Amora'im hold like Rav Ada.

Question (Shiltei ha'Giborim, ibid.): Why does the Tur totally exempt a Mu'ad that was guarded it minimally, unlike his father the Rosh?!

Poskim

Shulchan Aruch (CM 396:1): A minimal guarding suffices for a Mu'ad ox, and for Shen and Regel, which are Mu'ad from the beginning. Therefore, if one tied it with a Mosirah, or guarded it minimally, and it left and damaged, he is exempt.

SMA (2): The Rambam totally exempts; Tosfos and the Rosh exempt from full damage, but obligate half-damage. Regarding half-damage, we do not exempt more because it is Mu'ad.

Pnei Yehoshua (44b DH Omar): Rav Ada's reasoning is sound. We do not exempt more because it is Mu'ad. We asked incredulously (42b), you cannot say that a Mu'ad is exempt and a Tam is liable?! Why does Rav argue? We cannot say that it is a Gezeras ha'Kasuv, for we can explain the verse like Rav Ada! Rather, Rav disagrees because the Torah should have written 'if he will not guard' (without "it") to teach that the Tam side is still liable. We would know that it exempts only the Mu'ad side, but the Tam side (or an actual Tam) is liable. If a Tam were exempt, the Torah would have written this regarding a Tam, and the Gezeirah Shavah would teach to a Mu'ad. Rather, it says regarding Mu'ad "if he will not guard it" to totally exempt a Mu'ad. We can explain that the Torah requires less guarding for a Mu'ad because its damage is less common. Since it has a Kol, others know to beware.

Gilyon Maharsha: Rav Ada argues, and says that there is no reason to exempt a Mu'ad more than a Tam. A Mu'ad pays full damage only if it was not guarded at all.

Gra (1): The Rambam rules like Rav, for we do not follow a Talmid (Rav Ada) against his Rebbi. The Sugya on 55b is like Rav. Our Mishnah switched to flock, which damage only through Shen and Regel, to teach that a minimal guarding suffices. According to Rav Ada, it could not discuss Keren, for it still pays half! However, the Sugya on 39b is like Rav Ada.

Shulchan Aruch (ibid.): A Mosirah or a minimal guarding does not suffice for a Tam. One must guard it properly, i.e. a door that can stand even in an abnormally strong wind. A minimal guarding is a door that can stand only in a normal wind. If it cannot stand even in a normal wind, it is as if it is not guarded at all.