I'm interested in any ownership of a slave by a 'abstract' entity. Slaves are typically portrayed as the personal property of a man who also happens to own a plantation. But were plantations themselves ever treated as corporate persons or business entities, and if so could the plantation's slaves be considered property of the plantation, rather than the plantation owner? I realize that is a rather fine distinction, but modern corporations own all kinds of property like real estate and intellectual rights that are separate from the personal property of the CEO. I'm wondering whether the idea of corporate personhood is old enough to have been applied to slave ownership. Alternatively, lets say a slave works as a janitor in the Virginia state capitol building. Does that make the slave government property?
Corporate personhood didn't truly begin until 1886, well after slavery, in a case called Santa Clara County v. Southern Pacific Railroad Company (ref: 118 US 394 (1886)) where a unanimous court decided that corporations were citizens under the fourteenth amendment. They have progressively gained more and more right since then, and the ball really got rolling in the 1900s especially.
So unfortunately this is a fairly anachronistic question as corporate personhood and the types of concepts you're discussing really didn't exist during the era of slavery.
As for the government owning slaves, no. They were owned by individuals. If you look at slave-related records & databases - such as the Records of the Board of Commissioners for the Emancipation of Slaves in the District of Columbia (M520) - you find that, in this example in Washington, DC that a lot of the slaves that worked there were owned by people in other cities or even states. Interesting, right? So as to your second question, the answer would also likely be no (in most cases; there probably were some government owned slaves here and there).
I'm on my phone, so I'll have to keep this brief. Yazman is partly correct in that corporate personhood and ownership as you seem to define it is a postindustrialization concept, and the South was far from industrialized in the antebellum period. However, investors from the North and some "progressive" southern industrialists bought slaves from planters for company labor. These slaves were considered capital investments rather than labor expenses, as they were bought in a lump sum rather than paid wages over time. Despite comprising only 5% of slave labor in the South, industrialized slavery raised a number of issues for both the industrialists and their employees, sparking labor strikes and disturbing the hegemony of the planter class. If you want a case study, the Tredegar Iron Works strike may answer some of your questions.