Gemara

36b: A man hit Reuven. Rav Yosef ruled that he receives a half-Dinar. Reuven did not want it, and said 'give it to the poor'. He later retracted and asked 'give it to me. I will use it to make myself healthy.'

Rav Yosef: You cannot retract, for the poor already acquired it. Even though there are not poor people here, we are a Yad (power of acquisition) on behalf of poor people elsewhere;

(Rami bar Chama - Beraisa): Orphans do not need Pruzbul (a document in which one gives debts owed to him to Beis Din, so that Shemitah will not cancel them). R. Gamliel and his Beis Din are like the father of orphans.

Nedarim 59a (R. Aba): Since one can permit his vow, a vow is like a Davar she'Yesh Lo Matirim (something permitted in another situation), which is not Batel in a majority of Heter.

Question: One can permit a declaration of Terumah, yet it can be Batel!

Answer: The case is, the Terumah was given to a Kohen, so the Yisrael may no longer permit his declaration of Terumah.

Kidushin 28b (Mishnah): Saying 'I give this to Hekdesh' is like Mesirah (handing it over) to a person.

Rosh Hashanah 6a: "B'Ficha" teaches that Bal Te'acher (the Isur to delay bringing Korbanos) applies to Tzedakah.

Rishonim

Question: Why did Rav Yosef need to say 'even though there are not Aniyim here, we are Yad Aniyim'?

Answer #1 (cited by Rif): Normally, one can retract from a promise to give to the poor. Aniyim acquire like regular people. If Reuven told Shimon 'you owe me a Maneh. Give it to Levi', this works only b'Ma'amad Sheloshtam (if all three of them are there). The same applies to Aniyim. Rav Yosef said 'even though there are no Aniyim here to acquire through Ma'amad Sheloshtam, we are Yad Aniyim.'

Rebuttal (Rif): "B'Ficha" teaches that Bal Te'acher applies to Tzedakah. This shows that one is obligated through words. If not for 'we are Yad Aniyim', Reuven could have retracted. This is not because Aniyim acquire like regular people, rather, because Reuven had not yet received the half-Dinar. One can be Makdish now land that Beis Din will collect for him (Bava Metzia 7a), but not Metaltelim.

Answer #2 (Rif): Rav Yosef meant 'Aniyim are no less than others. Even though there are no Aniyim here, we are Yad Aniyim to acquire through Ma'amad Sheloshtam for them.' If one said about money in his possession 'it is for Aniyim', they acquire immediately, due to "b'Ficha".

Rebuttal (R. Efrayim): The Gemara calls Ma'amad Sheloshtam 'a Halachah without a reason (we cannot explain how it works).' You cannot say that it works when one of the parties is missing! If Reuven explicitly told Shimon 'you owe me a Maneh. Make Levi acquire it on behalf of Yehudah', it would not work. Here, Reuven did not explicitly tell Rav Yosef to acquire for Aniyim. All the more so it does not work! Also, according to the Rif, Rav Yosef could not rule about this, for judges of the city may not rule about Tzedakah for Aniyim of the city (for it lessens the burden on them)!

Answer #3 (R. Efrayim): We must say that Rav Yosef already received the half-Dinar. Reuven asked 'give it to me. I will use it to make myself healthy', i.e. I am like an Oni. Normally, once someone says 'give', it is as if he said 'acquire', even without Beis Din. Here is different, for he did not say to give to a particular person. He could not retract only because Rav Yosef was Yad Aniyim, so it is as if they already received it.

Rambam (Hilchos Nedarim 4:7): One may permit Nidrei Hekdesh just like one may permit Nidrei Isur.

Poskim

Shulchan Aruch (YD 258:6): One who vowed to Tzedakah cannot retract unless he asks a Chacham and the Chacham permits him.

R. Akiva Eiger (3): If one was Makdish to take effect after 30 days, he can retract within 30 days (Ran and Rashba, Nedarim 29b DH Hacha, DH Afilu).

Pischei Teshuvah (7): V'Shav ha'Kohen (18) concludes that one cannot retract from Tzedakah Toch Kedai Dibur, for it is like Hekdesh, and his Dibur is like Mesirah. Pnei Arye (41,42) says that if Reuven vowed to give to Ploni the Oni, and Ploni became rich, if Reuven already sent the money with Almoni, Ploni already acquired and Reuven cannot retract. If he did not yet send the money, he can regret the entire vow and permit it. It is not enough to say 'I would not have vowed had I known that Ploni will become rich', for this is Nolad. If he does not permit his vow, he must give it immediately. (Since Ploni does not need Tzedakah, he cannot benefit from it. He may give it to any Oni he wants, even one of his relatives.) Had Reuven vowed to give to Ploni because he is an Oni, he need not permit this.

Shulchan Aruch (12): If one said that he will give a gift to his friend, if the recipient is an Oni this is like Nidrei Tzedakah, he may not retract.

Beis Yosef (DH Kosav ha'Mordechai): The Mordechai (Bava Basra 498,499) permits retracting from a promise to give a large gift to an Ashir, but not to an Oni, for this is like a vow. This is only if the giver had the money at the time. If not, the vow does not take effect and he can retract, like it says in Bava Kama. I say that this is only regarding an object, but one who vows to give an amount to Tzedakah is obligated, even if he was penniless when he vowed.

Shach (25): R. Yerucham cites some who permit using a gift on condition to return it to fulfill an oath to give Tzedakah, but he disagrees. It seems that this does not suffice even if he did not swear (for it is like a vow). However, if one swore to give to an Ashir, he is Yotzei through such a gift.

Pischei Teshuvah (13): Keneses ha'Gedolah says a gift to a Ben Torah is a Mitzvah, just like Tzedakah - "Etz Chayim Hi la'Machazikim Bah." Shevus Yakov (2:159) says that if the Ben Torah has income, the giver can retract.

Shulchan Aruch (CM 243:2): If one told a Shali'ach 'take this money to Ploni', he can retract as long as Ploni did not get it. If Ploni is an Oni, he cannot retract (Rema - and even if he is rich, retraction is a lack of faith) if it is a small amount.

SMA (5): The Rema fixed a textual error in the Shulchan Aruch. Without the Rema's comment, the Shulchan Aruch allows retracting from a large gift to an Oni, and this is not true. A gift to an Oni is a vow, whether it is big or small. The Ir Shushan says that the distinction between big and small applies only to retracting a gift to an Oni. This is wrong.

Rema: If Shimon's wife gave a gift when she was sick and Shimon consented and later he wants to retract, if the recipient was an Oni, he cannot retract.