In the South, slaves typically could not own property - and if they could, it was at the leave of the master, but as with most US law - it depends on the state.

For example, the Virginia Slave Codes of 1705, title XV: "And also be it enacted, by the authority aforesaid, and it is hereby enacted, That no person whatsoever shall, buy, sell, or receive of, to, or from, any servant, or slave, any coin or commodity whatsoever, without the leave, licence, or consent of the master or owner of the said servant, or slave: And if any person shall, contrary hereunto, without the leave or licence aforesaid, deal with any servant, or slave, he or she so offending, shall be imprisoned one calender month, without bail or main-prize; and then, also continue in prison, until he or she shall find good security, in the sum of ten pounds current money of Virginia, for the good behaviour for one year following; wherein, a second offence shall be a breach of the bond; and moreover shall forfeit and pay four times the value of the things so bought, sold, or received, to the master or owner of such servant, or slave: To be recovered, with costs, by action upon the case, in any court of record in this her majesty's colony and dominion, wherein no essoin, protection, or wager of law, or other than one imparlance, shall be allowed."

In short, the only way a slave could own property was at the whim of the master...who could decide later to just confiscate it for themselves.

My first thought would be that it came from the period when slaveholders loved to paint themselves as benevolent stewards of the negro race, who were clearly incapable of managing freedom.