A woman named Frances Wright did something like what you are asking in 1824. In Memphis, TN she bought two thousand acres of land from Andrew Jackson and would buy slaves. On this land she set up a co-operative labor system where they could basically work off their price of purchase and then they would be set free.

EDIT: Forgot to mention that the name of this place was Nashoba. Nashoba is the Chickasaw word for "wolf."

Source: Gerald M. Capers Jr.'s The Biography of a River Town

The US Government did this in its own small way. The District of Columbia Compensated Emancipation Act in 1862 essentially purchased all slaves in the nation's capitol and set them free. Before that, the politician Daniel Webster loaned money to Paul Jennings, a slave owned by President Madison, so that he could buy his own freedom. Webster then found Jennings a job so that he could pay him back. The contract apparently stated:

"I have paid $120 for the freedom of Paul Jennings; he agrees to work out the same at $8 per month, to be furnished with board, clothes, washing." (you can see the contract here)

It's not exactly the scenario you describe but it is essentially the same thing: He helped put up the money to undermine the system of slavery and free at least one person from it. You can read Paul Jennings' memoir A Colored Man's Reminiscences which is in the public domain.

Just to clarify, are you asking about slavery in the US circa 17th-19th century? Or slavery throughout history in every culture?

A great example is that of Anthony Burns. In 1853, Burns escaped slavery in Virginia but was captured under the Fugitive Slave Laws in Boston. Abolitionists in Boston tried to protect him, both through legal council during a trial and through attempts at escape from prison, but eventually Burns was escorted back into slavery by federal troops. When returned to slavery, a group of abolitionists collected money to purchase his freedom but his owner initially would not sell. Eventually the owner did sell Burns to another man who sold him to the abolitionists and freedom.

edit: Source: Finkelman, P., & the Dictionary of Virginia Biography. Anthony Burns (1834–1862). (2013, November 21). In Encyclopedia Virginia. Retrieved from http://www.EncyclopediaVirginia.org/Burns_Anthony_1834-1862.

The first instance I can think of is with the Quakers. They did participate in buying slaves to free them during the 18th century but often ran into the adverse situation you described. An example of this is when the Manumission Society of North Carolina polled about 600 slaves which had been granted freedom to the Yearly Meeting by local Quakers. Most requested to return to Liberia and the society sent 40 slaves to Liberia, 120 to Haiti and another to Liberia. One ship headed to Liberia docked in New Orleans and the slaves were auctioned off. Those who disembarked in Haiti were met with resistance and they returned to North Carolina where many were eventually forced back into slavery.

The Kingsley Plantation would be the second to come to mind. The slave trade had been abolished shortly after he began transporting slaves from Africa in 1803. However, Florida (where the plantation is located) was still under Spanish rule and slavery was still permitted. Given this, Spanish law at the time established another class for freed slaves (whites, free people of color and slaves). This encouraged slaves to buy their freedom and own land, where many freed blacks would own other black slaves.

Zephaniah Kingsley allowed free blacks to live on his land while still owning slaves much of the time. He actually married a former slave (Anna Kingsley) and allowed her to oversee several of the plantations that he owned. She later supported the Union and became a symbol of the free black community. Anywho, I bring up Kingsley because although he did own and trade slaves, he would treat his slaves like employees rather than with the brutality we saw in Virginia, Mississippi, etc. His slaves were armed (and trained to protect themselves), provided with education, their cabins had padlocks (on the inside of the door) and their duties were often completed early in the day. Slaves were free to do as they pleased after the day's duties had been completed and often times, tasks would be withheld so that the slaves could gather their own crops, fish, etc.

Many historians argue that this was strictly an economical choice on his behalf but I do like Daniel Schafer's account of Anna Kingsley's life in Anna Madgigine Jai Kingsley: African Princess, Florida Slave, Plantation Slaveowner. When evaluating those closest to Zephaniah, we can see that he truly did care about the well-being of his slaves and what would become of them after they were sold. By giving them an education especially, he was ensuring that his slaves would be treated better by their next owner. He also sold slaves from his own land ensuring that only "dignified" customers were entertained (as if slavery could really be dignified, it's better than what we saw in other parts of the country). Also, when America acquired Florida, the northern race relations caused problems for Zephaniah and his wife. Instead of submitting to it, Anna and Zephaniah relocated to Haiti in 1835 where they founded a colony of sorts and this became a refuge for freed slaves.

It's not exactly the situation you described but given the time, the Kingsleys were pretty awesome in comparison to many others during the antebellum era.

There was a period in US history when it became somewhat prevalent for at least a minority of slave owners to free some or all of their slaves.

Since they had presumably bought them (or inherited them), I guess this counts.

This varied both in time and by state across the slave states.

There was a window in the early history of the USA when manumission of slaves became more popular and quite a few (though still only a small minority) of slaves were freed. Then this became less popular and less common.

I will just talk about manumission, or the freeing of slaves, in the State of Virgina.

Some 500 Virginia slaves won freedom by serving in Patriot Armies during the Revolutionary War. (Some 6,000 slaves also fled to the British during the war, of whom circa 2,000 were evacuated as free after the war, mostly to Nova Scotia.)

Until 1782, slaves could only be freed in Virginia with the consent of the colonial legislature. In 1782 it became legal for a slave owner to voluntarily free their slaves through a process known as “manumission”. (As long as the slave owner had no debts which creditors might be relying on the value of the slaves to repay.)

Manumissions increased radically after this law was passed (despite the fact that the large plantations were chronically indebted). The free black population in Virginia went from 2,000 in 1782 to 20,000 in 1800 (from 1% of all blacks to 7%). Some of the manumitters were liberal critics of slavery, others were religious critics of slavery such as Quakers or evangelicals.

Many freed slaves in their wills, rather than in their lifetimes. Richard Randolph, for example, died age 26, and his will freed 72 slaves and gave them 400 acres of land (one fifth of his plantation) for their settlement.

George Washington was a supporter of the gradual emancipation of slaves, and in his will freed all of his slaves on the death of his wife Martha (though she actually freed them early, about 12 months after Washington died).

(Note: Washington had a complex (and tragic) set of decisions to make around freeing his slaves. He owned 123 slaves at Mt. Vernon at the time of his death, but another 153 slaves were the "dower slaves" of his wife Martha. The dower slaves belonged to the estate of Martha's deceased first husband. She (by his will) had the use of them during her lifetime, but they would go to his other heirs upon her death. Washington could not free the dower slaves who were heavily intermarried with his own slaves. He stopped selling slaves (so as not to break up families) but decided not to free his own slaves until after the fate of the dower slaves was out of his own and Martha's control).

There were several attempts made to abolish slavery in Virginia. In 1785 the Methodists got a bill before the state legislature, but it was defeated and at the same time manumission was almost overturned. This made the Methodists retreat from anti-slavery activity.

The slave revolt in San Domingue from 1791 to 1804 caused great alarm in the slave owning American South. Fears of slave revolt spread. People became more worried about growing numbers of free blacks (seen by some as potential instigators or ringleaders of slave revolt).

In 1806, Virginia amended the manumission law. Slaves could still be freed, but now newly freed slaves had to leave the state within one year of manumission and not return. This had a chilling effect on manumission, as many slaves (and slave owners) did not want to be forced to move away from family and connections on being freed.

There was a window from about 1780 to 1806 when revolutionary liberal sentiment caused slave owners to question the morality of slavery. Some tried to abolish slavery in the South (usually in a gradual system) while others freed their own slaves. The anti-slavery sentiment was never a majority in the South, but it was a minority that was considered and listened to.

After 1806, southern sentiment turned more against abolition. Cotton Plantations (only possible on a large scale after the invention of the Cotton Gin in 1794, and only practical from 1800 onwards) gave a new economic impetus to slavery in the South.

Thereafter, abolitionist voices became less mainstream and the South committed more and more to maintaining, supporting and defending the slavery system.

Source: Alan Taylor, “Slavery and War in Virginia, 1772-1832, The Internal Enemy” 2013

Some of these answers seem to imply that yes, this did occur in some form or another here and there. History ignoramus follow up question:

Would this have done any long term good, or would it simply be further supporting the slave trade and encouraging more slavery overall? I'm mentally comparing this to the idea of buying all the ivory on the market as an attempt to end the ivory trade. Were new slaves still being brought over from Africa leading up to the civil war? Would slavemasters deliberately promote high birth rates among their slaves if they thought demand was increasing?

Yes it most definitely did happen. Perhaps most famously, Frederick Douglass gained his legal freedom in the mid-1840s while living in Britain. A number of British abolitionists helped raise money to buy Douglass' freedom from Thomas Auld. Another good example would be Gerrit Smith, radical abolitionist, founder of the Liberty Party, and funder of John Brown's raid, who purchased the freedom of a number of slaves from a Virginia slaveholder in the 1840s. He was roundly criticized by William Lloyd Garrison and some other moral suasion abolitionists who claimed he was reinforcing the idea of slavery by buying a slave - Smith simply replied that he'd do whatever he could to free slaves, even if that meant conceding that slaves were defined as property in the South.

See James Oakes, The Radical and the Republican on Douglass (among myriad others) and Norman Dann, Practical Dreamer or John Stauffer, The Black Hearts of Men on Smith.

I don't have the sources, but both Brazilian emperors (Pedro I and Pedro II) did it a couple times

I know it happened to Sojourner Truth. If I recall correctly, she and her child ran away from her master and found refuge with a white family. When her master caught up with her, the family bought her and her child for $15, then promptly freed them.