Private corporations also kept slaves, and some corporations were owned by blacks, and bought slaves, often the women and family of the owners.
Many of the slaves were, like Fredrick Douglass, the offspring of their owners, and some owners had as their business model the sale of their children. It was indeed a peculiar institution.
It was a global institution as well, many Americans seem to have the impression this was the only country with slavery/ it was also not the last to have it. There were French or British possessions that had slavery right up to the end of the century.