Can be done, just not the easy way. It usually involved driving piles through the slab and waaaay down into the ground, or injecting grout or cement into the soil underneat the slab.
Brad
I know all about grout injection. But that only works in/on stable soils. If you inject grout to level a structure that's resting on expansive clay soil -- you still have a structure that's resting on expansive clay soil and the next time it rains (or dries out, depending on the condition of the soil when they do the injection) ... the problem starts all over.
Driving piles
through the expansive clay to a stable substratum is a possibility, but how do you drive piles through a completed house and, once the piles are in place, how do you anchor the foundation to the piles to isolate the structure from the expansive clay underpinnings?
Best approach, IMHO, remains to get your money back (if possible) and move on.