They may get beaten or whipped to death, but they can still quit. When you have a family to feed (and the threat of deportation) you don't have the luxury of making a principled decision to refuse. Slavery is a spectrum, not a red line drawn just short of some entrepreneur's convenience.
As for LOS&D not working when cheap illegal foreign labor floods in, well, what better example of supply and demand can you offer? Lots of people want to sell their labor, but only a few want to buy it. That situation did not just happen due to blind market forces, it was planned and deliberately engineered, over and over, whenever America needed cheap labor. And when the cotton was picked, or the railroads finished, or the factories shut down, or the harvest brought in, we told all those furriners to 'go back to your own country'.
You just can't seem to grasp the self-serving shallowness of your own superstitions.
You do know who the 'hoodoo' running away was, don't you?