Constitutionally, after a little scuffle in the mid 1800's, a person or business can't own an employee. Other than that not really, we usually got to strike and revolt if we want anything, but they keep us so poor that it makes it an untenable option.
But they can still be rented from the government which can still own people as long as they had some drugs planted on them, right? I mean you just went into Slavery-as-a-Service instead of a proper ownership model.
This is true. And in true capitalist nature, the overhead of owning people (paying for room and board etc) can be socialized, while the fruit of their Labor is privatized and made available to well-connected corporations.