u/Georgy_K_Zhukov has already answered this question for the US South, but I can add a few remarks about pre-revolutionary Haiti, aka Saint-Domingue. This does not concern anti-slavery advocates, just people who wanted to free people they knew, and bought them to do so.
In Saint-Domingue, the practice of buying enslaved people in order to free them appears to have been quite common. This was due to the particular demographics of colonial Saint-Domingue: lacking European women, French settlers had found companionship with African slaves, and later free Creoles - black or mixed-race. Notwithstanding the asymmetry of such relationships, the fact is that they resulted in many offsprings. For some of these men, for whom France was no longer home, their families were there, in Saint-Domingue, and they were "coloured". On the eve of the Revolution(s), the "free coloured" population was almost as large as the white one, and had been able to accumulate wealth and gain power, much to the chagrin of some whites. This also resulted in complicated situations, where families included whites (free), mixed-race people (free and enslaved) and blacks (usually enslaved, some free). So what did happen is that the free relatives of enslaved people bought them - with the approval of the slave owner - to free them later. King (2001), studying 606 notarial acts of manumission, has found 61 that were clearly acts of people buying the freedom of a slave, and sometimes the enslaved person was able to self-purchase. He cites several examples:
Barbe ditte Leonore freed her godmother, Guittonne, aged 66, in 1780, having obtained her in 1774 from Mme Dalcourt de Chambellan. She cited "benevolence, friendship, and good services received from the said slave" in the act of manumission, which was granted free of tax in recognition of the advanced age of the subject.
Often, says King, future manumission was made an explicit condition of the sale, to prevent possible reenslavement if something went wrong with the buyer.
Militia noncommissioned officer Pierre Amoune sold to his old commanding officer, Jean Baptiste Malic, or Mali, a 9-year-old female creole slave named Marguerite for 1,000 livres in 1778. The little girl was described in Malic's marriage contract, though not in the act of sale, as Malic's natural daughter. A condition of the sale was that Malic free the little girl within two years, or the sale would be voided.
This is something that Toussaint Louverture did right after his own emancipation in 1776: he bought a slave named Jean-Baptiste and granted him his freedom (though why he did that is unknown) (Girard and Donnadieu, 2013).
Some slave owners were not opposed to the practice as it allowed them to get rid of older slaves without having to pay the manumission tax (which could be as expensive as a new slave) since it was the slave's kin who paid not only for buying the slave but also the tax. It was a win-win situation: families got their kin free while the slave owner not only was rid of a useless slave, but was paid for it, tax-free, so that he could by a new one. Some slave owners even granted "irrevocable permission" to anyone acting on behalf of the slave to start the manumission procedure. The enslaved person could do that through a third party, and buy themselves their freedom. Authorities were not favourable to this sort of practice as manumissions had been a leading cause for the increase in the free coloured population.
Sources
Girard, Philippe R., and Jean-Louis Donnadieu. ‘Toussaint before Louverture: New Archival Findings on the Early Life of Toussaint Louverture’. The William and Mary Quarterly 70, no. 1 (2013): 41–78. https://doi.org/10.5309/willmaryquar.70.1.0041.
King, Stewart R. Blue Coat Or Powdered Wig: Free People of Color in Pre-Revolutionary Saint Domingue. University of Georgia Press, 2001. https://books.google.fr/books/about/Blue_Coat_Or_Powdered_Wig.html?id=JX_SbvLE2_YC.
It did happen, but it was very rare. This older answer touches on a prominent example.