Gemara

(Rav Acha bar Yakov): If one makes Kidushin on Tnai (with a stipulation) and has Bi'ah, all agree that a Get is not required.

Question (Rav Acha brei d'Rav Ika - Beraisa): A mistaken Chalitzah is valid.

(R. Yochanan): This is when they tell the Yavam 'do Chalitzah on condition that she will give you 200 Zuz.'

Since he does the act of Chalitzah, he pardons the Tanai. Here also, since he has Bi'ah, he pardons his Tanai!

Answer (Rav Acha bar Yakov): All Tana'im are learned from the stipulation with Bnei Gad and Bnei Reuven. (They were given Ever ha'Yarden on condition that they help conquer Eretz Yisrael);

A Tnai is binding only if the act (that is contingent on it) can be fulfilled through a Shali'ach. (Chalitzah cannot be done by a Shali'ach. This is why the Tnai is void, not because he pardoned it.)

Question: There is no Shelichus for Bi'ah, yet Tnai works for Kidushei Bi'ah!

Answer: A verse teaches that all actions that make Kidushin have the same law. (Kidushin through money or a document can be done through a Shali'ach.)

Yevamos 52b (Beraisa - Rebbi): If a Yavam was Mekadesh his Yevamah after Chalitzah:

If he intended for regular Kidushin, she needs a Get. If it was like Kidushin of a Yevamah, she does not need a Get;

Chachamim say, in either case she needs a Get.

53a (Rav Ashi): Chachamim hold that one can stipulate about Chalitzah. Rebbi holds that one cannot. (The Tnai is Batel, and the Chalitzah is valid in any case.)

Objection (Ravina): All hold that one can stipulate about Chalitzah! Rather, the Tnai was not Kaful (it did not say what will be if the Tnai is not fulfilled), They argue about whether or not such a Tnai is valid.

Rishonim

Rambam (Hilchos Ishus 6:1): Every Tanai, in Kidushin, divorce, sales or other monetary laws, needs four things...

Rambam (2): The Tnai must be Kaful. The 'if' must precede the 'if not'. The Tnai must precede the action (that is contingent on the Tanai). It must be possible to fulfill the Tanai.

Question (Ramach): Why did the Rambam omit that Tnai helps only if the action can be fulfilled through a Shali'ach?

Answer (Magid Mishneh and Gra CM 241:36): He already taught (Hilchos Yibum 4:24) that Chalitzah is valid even if the Tnai was not fulfilled. Here he discusses only the Tnai itself.

Rebuttal (Kesef Mishneh): If the Rambam learned from Bnei Gad that a Tnai works only if the action can be fulfilled through a Shali'ach, he would have taught so here! Rather, he is Machshir Chalitzah even if the Tnai was not fulfilled, because when he did the action, he pardoned the Tanai. Rav Acha bar Yakov does not require a Get when one made Kidushin on condition and had Bi'ah. We challenged this from a Beraisa that is Machshir a mistaken Chalitzah. I.e., since he does the act, he pardons the Tanai; the same should apply to Bi'ah! Rav Acha answered that we learn Tana'im from Bnei Gad, in which a Shali'ach could do the act. Tnai helps for Bi'ah, for we equate all acts of Kidushin. We do not rely on this poor answer. The Halachah does not follow Rav Acha, rather, like the challenge. Chalitzah (and Bi'ah) take effect even if the Tnai was not fulfilled, because he pardoned the Tanai.

Lechem Mishneh: In Yevamos, Ravina said that all agree that a Tnai works for Chalitzah. This shows that the requirement that a Shali'ach could do the act is not universally accepted. However, why doesn't the Rambam mention regarding monetary Tana'im that one who did an act pardoned the Tnai (unless he stipulated at the end of the act)? Also, if one was Mekadesh on Tnai and has Bi'ah Stam, we require a Get due to Safek. We should say that also Chalitzah on Tnai is Safek (perhaps he did not pardon the Tanai)! The Magid Mishneh's answer is primary.

Sha'ar ha'Melech (DH uv'Hachi): Perhaps we are concerned lest he did not pardon his Tnai only regarding Bi'ah. Since he made a proper Tnai (when it is needed) at the time of Kidushin, he saw no need to repeat it at the time of Bi'ah. Regarding Chalitzah, he stipulated beforehand but did not mention it at the end of the Chalitzah, so surely he pardoned it. However, we should also say that one who gives a Get pardons his Tanai! Rather, since Chalitzah is a Mitzvah, we assume that he pardoned his Tnai to fulfill the Mitzvah. Alternatively, mid'Oraisa no intent can disqualify Chalitzah. Mid'Rabanan, we require intent to permit. We are lenient about a Safek whether or not he pardons his Tanai. Alternatively, the Rambam rules like Rav Ashi, who allows Tnai v'Ma'aseh b'Davar Echad (the Tnai contradicts the act, e.g. this is your Get on condition that you return it to me) because we learn from Bnei Gad only matters such as Tnai Kaful, which Moshe was particular about. We do not learn about Tnai v'Ma'aseh b'Davar Echad, or that a Shali'ach could do the action, because it just happened that this was the case.

Tosfos (Kesuvos 74a DH Tanai): Throughout Shas, we hold that a Tnai works only if the act could be done through a Shali'ach. It is astounding to say that Ravina disagrees! Rather, Ravina explains that if Chalitzah was done on Tnai and it was not fulfilled, mid'Rabanan some Zikah remains. If afterwards a Yavam was Mekadesh her with 'Zikas Yibum' (i.e. Ma'amar), she needs a Get.

Pnei Yehoshua (Gitin 75a DH v'Yesh Lomar): Tosfos holds that if he controls the act and can do it through a Shali'ach, he can stipulate about it. It seems to me that if he controls it, this is a Ma'aseh, and a Tnai (speech) cannot Mevatel it! I would say that a full Ma'aseh is one that cannot be done by a Shali'ach, e.g. a bodily act like Bi'ah or Chalitzah. A Tnai cannot stop it. However, this is unlike Tosfos. (It is like the Mordechai, Kesuvos 290.)

Chasam Sofer (EH 2:90 DH v'Ra'isi): If so, a Tnai should annul a weak Ma'aseh! However, a Tnai that contradicts the Ma'aseh is Batel. The Rambam does not disqualify a Tnai that contradicts the Ma'aseh. Perhaps this is why he is not concerned whether or not a Shali'ach can do the Ma'aseh.

Note: If so, he should teach that a Tnai always invalidates such a Ma'aseh!

Chasam Sofer (ibid., DH Aval and DH v'Hinei b'Ta'am): Even when Tnai does not help, e.g. when a Shali'ach could not do the action, Tnai helps regarding Mitzvos. E.g. one who wears two pairs of Tefilin (or sits in a Sukah on Shemini Atzeres) due to Safek should stipulate that he does not intend to be Yotzei with the Pasul Tefilin (or if this is not the time for the Mitzvah), to avoid Bal Tosif. This is because most Mitzvos can be done through a Shali'ach, even if this one cannot, and a Shali'ach can give the reward. If normally a Shali'ach can do the action, we are not concerned if in this case he cannot, e.g. a Kinyan involving minors.

Rosh (Yevamos 12:15): Letter of the law, no Tnai should be able to uproot an action, even if the Tnai was not fulfilled. We learn from Bnei Gad that it can. Therefore, it must be similar, i.e. the action can be fulfilled through a Shali'ach. Yehoshua was Moshe's Shali'ach to give to them Eretz Gil'ad only if they fulfill their Tanai.

Rosh (Gitin 6:9): Even when one says 'Al Menas', we require (a Tnai Kaful and) that the action could be fulfilled through a Shali'ach. We learn from a tricked Chalitzah, in which we say 'do Chalitzah Al Menas that she will pay you 200 Zuz.'

Poskim

Shulchan Aruch (EH 38:2): Every Tnai needs four things. The Tnai must be doubled. The 'if' must precede the 'if not'. The Tnai must precede the action. It must be possible to fulfill the Tanai.

Shulchan Aruch (CM 241:12): A Tnai about a gift is valid only if meets the conditions given in EH 38.

Gra (36) and Beis Shmuel (EH 38:6): We also require that the action can be fulfilled through a Shali'ach. The Shulchan Aruch relies on what he wrote in Hilchos Chalitzah (below).

Shulchan Aruch (EH 169:50): A tricked Chalitzah, in which they tell him that that if he does Chalitzah she will pay him 200 Zuz, is Kosher. This is even if she does not pay, and even if he made a Tnai Kaful.

Beis Yosef (DH u'Mah she'Chosav Afilu): Rashi explains that since Chalitzah cannot be fulfilled through a Shali'ach, a Tnai does not work, so the Chalitzah is Kosher. Also the Rosh says so, and the Rambam rules like this.

Note: This sounds like the Rambam agrees with Rashi's reason. Perhaps the Beis Yosef retracted from what he wrote in the Kesef Mishneh, or was concerned for the Magid Mishneh's opinion.