Gemara

(Mishnah): (Damages apply to) specific property.

(Ravina): This excludes if Reuven's ox damaged, and Reuven made it Hekdesh or Hefker. He is exempt.

Support (Beraisa - R. Yehudah): Even if the owner made his animal Hekdesh or Hefker after it damaged, he is exempt. "The owner was warned, and it killed" - the killing and bringing to trial must like one.

Question: Is this enough? We should also require the final verdict in the same status, for "the ox will be stoned" is the final verdict!

Correction: Indeed, the killing, trial and final verdict must be like one.

33a (Beraisa - R. Yishmael): The ox is evaluated in Beis Din.

R. Akiva says, the victim takes the ox (it was his from when it damaged).

R. Yishmael holds that the victim is like a creditor. The damager owes him money. R. Akiva holds that they are partners in the ox that damaged. They argue in a case when the victim made the damaging ox Hekdesh. (It takes effect only according to R. Akiva.)

(Beraisa): If a Tam damaged, before Beis Din judges the case, if it was made Hekdesh, this stands.

It is not really Hekdesh. Hekdesh takes effect only for R. Avahu's law.

(R. Avahu): (If one was Makdish his property with a lien against it, really, it is not Hekdesh. The creditor takes the property, and pays a small amount to Hekdesh. It is not a real redemption.) This is a decree, lest people say that Hekdesh becomes Chulin without redemption.

44b (Mishnah): We kill the ox of a convert who died without heirs (if it killed);

R. Yehudah says, we do not kill it, for it has no owner.

(Beraisa): 'Ox' is written six extra times, to teach about six oxen that we kill (if they killed)... a wilderness ox, the ox of a convert who died without heirs;

R. Yehudah says, we do not kill them, for they have no owners.

(Rav Huna): R. Yehudah exempts even if it had an owner, and he made it Hefker or Hekdesh after it gored.

Chachamim count separately an ox of the wilderness and the ox of a convert, even though both are Hefker, to teach that even if it had an owner, and he made it Hefker or Hekdesh after it gored, R. Yehudah exempts.

Rishonim

The Rif and Rosh (1:16) bring the Gemara on 13b.

Rosh: Even though Chachamim argue with R. Yehudah, Ravina established the Mishnah like an individual, because Chachamim argue only about an ox that killed a person. All agree about an ox that killed an ox.

Question (Piplulei Charifta 40): When does a Mu'ad pay from the Aliyah, i.e. more than the damager is worth? Surely, the owner will be Mafkir it!

Answer #1 (Gilyon Maharsha CM 406:3): If the ox was lost, the owner cannot be Mafkir it.

Answer #2 (based on Hagahos Tur ha'Shalem CM 406:4): The Ra'avad and R. Yonason (brought below) hold that the exemption is only for a Tam (the Ra'avad learns from a verse discussing a Tam. However, Achiezer (3:41:3) holds that they exempt also a Tam.)

Answer #3 (Achiezer ibid.): He cannot be Mafkir it due to the victim's lien on it.

Rambam (Hilchos Nizkei Mamon 8:4): If Reuven's ox gored, and Reuven was Makdish or Mafkir it, he is exempt. One is liable only if it had an owner at the time of killing and when it is brought to trial.

Lechem Mishneh: The Magid Mishneh says that the Rambam rules like R. Yehudah. This is wrong. Regarding stoning (10:6), he rules like Chachamim! Rather, even though the Halachah does not follow R. Yehudah, regarding damages we learn from his reasoning.

Question (Tosfos Yom Tov 1:2 DH Nechasim Meyuchadim): R. Yehudah expounded a verse about stoning. Since we do not hold like him regarding stoning, why do we hold like him regarding damages?

Answer #1 (Tosfos Yom Tov): We do not need his verse to teach about stoning, for the extra occurrences of "ox" obligate stoning a Hefker ox. Therefore, we use his verse to teach about damages.

Answer #2 (Rashash, R. Chayim ha'Levi and Even ha'Ezel, cited in Kehilas Yakov 14:1): We expound like R. Yehudah regarding liability to pay also regarding death, i.e. Kofer, which is an obligation on the owner. Only regarding stoning, which is an obligation on the ox, we expound the extra occurrences of "ox" to obligate a Hefker ox, like Chachamim.

Me'iri (13b DH Shor): Even if the owner was Mafkir it after the trial began but before the final verdict, and Shimon acquired it, he is exempt. It must have an owner also at the time of the final verdict. The Rambam requires an owner only until it is brought to trial. We discuss only a Mu'ad. One could be Makdish a Tam, but Hefker would not work, for the owner and victim are partners, like R. Akiva taught.

Rambam (7): If (a Tam damaged, and) the owner was Makdish it, it is Kodesh, lest people say that Hekdesh becomes Chulin without redemption.

Question (Achiezer 3:41): R. Yehudah holds that a Mu'ad pays half like a Tam, and also the other half. Hekdesh should exempt from the Tam half!

Answer (Achiezer DH u'Lfi and (3)): It is a Gezeras ha'Kasuv that Hekdesh of a Mu'ad exempts from paying. It uproots the victim's lien. Hekdesh of a Tam does not uproot the lien, so it does not truly take effect. The Rambam (Hilchos Erchin 7:14) holds that even Kedushas Damim uproots a lien. Yad ha'Melech explains that the Hekdesh takes effect, but the lien returns when it is redeemed. Therefore, no one will pay to redeem it, so it has no value to Hekdesh, and hence no Kedushah. This is why it is a mere stringency to pay to redeem it. However, liability for one's ox ceases once it becomes Hekdesh, so it really is Hekdesh! The Rambam must hold that the exemption is only for a Mu'ad! However, in Hilchos Nizkei Mamon, he connotes that it is even for a Tam. He must explain like Rashi, that he cannot be Makdish it for it is not (now) in his Reshus, even though if the Hekdesh would work, it would uproot the lien and it would be in his Reshus. The Ra'avad who commented on the Rambam holds that Hekdesh takes effect. The Shitah Mekubetzes must be citing a different Ra'avad (who exempts even for a Tam). However, how can the former Ra'avad explain why Hefker works? Perhaps this is when the victim agreed to take money, for this releases his lien.

Rambam (10:6): We stone a Hefker ox, even though it has no owner.

Ra'avad, in Shitah Mekubetzes 13b: If he was Mafkir or Makdish it before the trial, he is exempt. We learn from "they will sell the ox and divide its money", that it has an owner at the time of payment.

R. Yehonason, in Shitah Mekubetzes 13b: We learn about a Tam that gored an ox from a Tam that gored a person.

Poskim

Shulchan Aruch (CM 406:3): If Reuven's ox gored, and he was Mafkir it, and Shimon acquired it, he is exempt. However, if Reuven was Mafkir it and acquired it back from Hefker, he is liable.

Prishah (2): It suffices that it had an owner at the time it killed and at the time of the final verdict.