For this subject, you might consider Buying Freedom: The Ethics and Economics of Slave Redemption, published by Princeton University Press. It's a fairly technical work, but it provides a comprehensive answer for slavery around the world. For a more readable work, try The Price of Freedom: Slavery and Manumission in Baltimore and Early National Maryland.

In the United States, purchased manumission in the early 19th century was a sort of middle ground between the emancipation movements of the North and the absolute slavery of the deep South. It was most common in the border states ─ Virginia, Kentucky, Maryland and Delaware ─ but it became more common across the United States as the century progressed.

In short, it was a process by which skilled slaves hired themselves out and earned wages that would then go to their masters and be considered a payment on an installment plan for their emancipation or that of their family members. These agreements could be found in wills ─ it was a way to ensure the liberation of a favored slave without crippling the financial prospects of your descendants ─ and in everyday business.

Hiring out skilled slaves was a common practice in the American South. A cooper or bricklayer might not always be needed at a particular plantation, but his skills could be useful elsewhere. The person needing the work would pay the slave's owner for the work, and generally that owner would in turn pay the slave for the work, keeping some fraction of the payment for himself.

If this sounds surprisingly egalitarian, you're a sweet summer child.

Purchase arrangements were tools for repression as much as they were for liberation. Given the prospect of freedom, a slave would be incentivized to work harder and longer hours. He or she, knowing that legal freedom was possible, would be less likely to run away and risk illegal freedom.

Purchase agreements could be designed to stretch out over decades. It might take 30 years for a person to earn enough money for his or her freedom, while the slaveowner received cheap, hardworking labor all that time without the risk of a runaway.