Gemara

(Beraisa - R. Noson): In a place where the custom is to return Kidushin money, we return it. Where it is not returned, we do not return it;

Rebbi says, a tradition from Sinai teaches that in a place where the custom is to return it, we return it. Where it is not returned, we do not return it.

They argue in a case when she died, about whether Kidushin money is given l'Tivu'in (to stay, even if she dies before Nisu'in). R. Noson says that Kidushin money is not given l'Tivu'in. Rebbi says that it is.

(Rav Papa): The Halachah is, whether he or she died or he retracted, Kidushin money is not returned. If she retracted, it is returned.

(Ameimar): Kidushin money is not returned. This is a decree lest people say that the Kidushin was mistaken (and never took effect), and that he can be Mekadesh (and marry) her sister.

(Rav Ashi): We are not concerned for this. Since he gives a Get, all know that he cannot be Mekadesh her sister.

Rejection: Perhaps someone heard that the Kidushin money was returned, but did not hear about the Get.

Kesuvos 76a (Rav Yehudah): Shmuel learned from the Mishnah about a Kalah to one who traded a cow for a donkey, and found that it was dead.

(Rav Nachman bar Yitzchak): He discusses an Arusah. Even the opinion that Kidushin money is not returned says so only about a Vadai Kidushin. Regarding a Ta'os, if the father cannot bring a proof he must return the money.

Question: A Beraisa teaches that if a buyer already paid for an animal, he must prove that it was Tereifah to recover his money. According to Shmuel, the seller should need to bring a proof to keep his money!

(Rami bar Yechezkel): Rav Yehudah erred. Rather, Shmuel said that the burden of proof is on the one in whose Reshus the doubt arose. The entire Mishnah of a Kalah supports this (like Rava explained).

Rishonim

Rif and Rosh (9:13): The Halachah follows Ameimar. Kidushin money is never returned.

Rambam (Hilchos Zechiyah 6:18): If one was Mekadesh a woman, even with 1000 Dinarim, if either retracted or died, the money is not returned. It is an absolute gift.

Rambam (19): If it was Kidushei Ta'os, the money is returned.

Magid Mishneh: This is when he thought that it is Kidushin, and it was something one could err about. If one was Mekadesh his sister, he knew that it is not Kidushin (and the money was a gift or deposit).

Mordechai (Kidushin 535): If one divorced his Arusah, the Gemara concludes that he cannot get back the Kidushin money, whether he or she initiated the quarrel. This is a decree lest people say that there was no Kidushin, and he may marry her sister in her lifetime. Tana'im argue about whether Kidushin was given l'Tivu'in, i.e. as if it sank in the sea and will not return. There was no final ruling. If Kidushin was conditional and the Tanai was not fulfilled, or it was Safek Kidushin, all agree that Kidushin money is not given l'Tivu'in.

Poskim

Shulchan Aruch (EH 50:1): If one was Mekadesh a woman, whether he or she retracted or died, or he divorced her, the money is never returned. Even if he was Mekadesh her with 1000 Dinarim, it is an absolute gift that is not returned. If it was Kidushei Ta'os, the money is returned.

Chelkas Mechokek (1): The Tur and Rambam omit 'or he divorced her', for this is how he retracts! The Shulchan Aruch taught both. We must say that it discusses divorce when she became forbidden to him. One might have thought that we fine her and she must return the money.

Chelkas Mechokek (2): It is a gift, even though presumably, he intended to give the money only on condition that there will be Nisu'in, and it should be returned even if he died, and all the more so if she retracted.

Shulchan Aruch (ibid): The same applies if she (was an orphaned minor and) did Mi'un (annulled a marriage mid'Rabanan), or the Kidushin was conditional and the Tanai was not fulfilled, or if it was Safek Kidushin.

Beis Yosef (DH v'Chosav ha'Ramban, citing the Ramban): A Ga'on says that if she if she did Mi'un, the money is returned, for then he may marry her relatives and she may marry his relatives. We want people to say that he can be Mekadesh her sister (lest he be Mekadesh her, and people think that it has no effect)! If a minor is divorced, since he is forbidden to her relatives, the decree applies. Also the Nimukei Yosef (DH Aval) says so.

Chelkas Mechokek (4): If there was Safek Kidushin, a Get is needed. We should be concerned lest people say that he can be Mekadesh her sister! The Mordechai proved from Kesuvos that money of Safek Kidushin is returned. However, that is not the conclusion. Rami bar Yechezkeil rejected it. Also, perhaps Rav Nachman bar Yitzchak does not hold like Ameimar, who decrees that Kidushin money is never returned. Safek Kidushin is no less than Kidushin mid'Rabanan of a (orphaned) minor. If a minor is divorced, the money is not returned due to Ameimar's concern! This is why the Rambam mentioned Kidushei Ta'os, but not Safek Kidushin.

Beis Shmuel (5): The Shulchan Aruch learned from the Mordechai. I say that the Mordechai means that if surely Kidushin money is l'Tivu'in, it would be returned even when there is no concern, e.g. after Nisu'in. Surely Safek Kidushin is not given l'Tivu'in, so if there is no concern, it is returned. The Shulchan Aruch understood that it is returned in any case of Safek Kidushin. This is difficult. Perhaps he understands that Rav Papa and Ameimar hold that Kidushin money is given l'Tivu'in, and they argue about whether they fine her to return it when she retracts. When it is not l'Tivu'in, e.g. Safek Kidushin, all agree that we do not uproot his rights due to the concern. What I said above is primary.

Gra (4): Rashi (Kesuvos 76b DH Aliba) says that Safek Kidushin is like Kidushei Ta'os regarding returning the money.

Rema: This refers only to Kidushin. From Nisu'in, the money returns.

Darchei Moshe (1): The Maharil (61) says so. Kidushin does not return, for we are concerned lest people say that it was Kidushei Ta'os. There is no such concern from Nisu'in, therefore, the money returns. He ruled like this in an actual case.

Chelkas Mechokek (5): It seems that the Rema discusses when she retracted and rebelled against him. Then the money returns, for he did not give it with intent that she rebel against him. If he died or retracted, surely it does not return. He must even pay a Kesuvah! Must a father who received Kidushin money return it when the Chasan dies or divorces her?! The Maharil discusses when she died. Letter of the law, her husband inherits her. There was an enactment that if she dies within the year, he returns half the dowry (Rema 53:3). In this case the Maharil ruled that the Chasan gets back the pre-nuptial gifts that he sent to her, and even the Kidushin money. The enactment was only to return half of what she brought into the marriage. One might think that she acquired Kidushin money at the time of Kidushin, and it is as if she brought it into the marriage; the Maharil says otherwise. Surely he did not mean that every widow or divorcee returns the Kidushin money. Maharam Lublin (19) says that the Maharil says that the Kidushin ring is returned and it is appraised in the Kesuvah, and this is the custom in some congregations. This is difficult. Why is the ring different from gifts that others give to her, which are hers?! The Rema holds like I said; he should have explained more clearly. Perhaps he relies on what the Shulchan Aruch wrote above, that Kidushin money is an absolute gift that is not returned.

Beis Shmuel (1): Maharam Lublin (19) says that Ameimar holds that Kidushin money is not given l'Tivu'in, but we decree that it is not returned, lest people say that he can be Mekadesh her sister. Maharil holds that Kidushin money is returned even if he died or divorced her after Nisu'in, for it is not l'Tivu'in, and Ameimar's concern does not apply. The Rema holds like this, and unlike Chelkas Mechokek. Maharam Mintz (96) says that the money is like a gift for her to adorn herself with, which is returned (Rema 99:2). R. Yerucham says that if she was forbidden to him by a Lav, just like he pays a Kesuvah when he divorces her, she keeps the Kidushin money. This connotes that if she was forbidden mid'Rabanan, and gets no Kesuvah, she returns the Kidushin money. He must hold that there is no concern after Nisu'in. If an Arusah returned the money, people would assume that it was Kidushei Ta'os; they would not say that this was a fine. All these opinions hold that there is no concern after Nisu'in. Mahari Veil (20) and She'eris Yosef (43) say that we are concerned even after Nisu'in, and the money is not returned. The Mordechai says that it is not returned not due to Ameimar's concern, rather, for we never resolved whether Kidushin is l'Tivu'in, so she need not return it due to Safek. I say that if a minor was divorced even after Nisu'in the money is not returned, lest people say that she left through Mi'un and he is permitted to her relatives.