Can a home rest permanently on two steel beams?
Those steel beams will still rest on the clay which is still shifting but they are used to reinforce the house and allow it to move off to the side for a bit while the machines go and drive in the piles and pour the new foundation. 

On note of the piles, they may not actually reach down to bedrock but instead go down and hold a chunk of clay. This means that more ground needs to move before the house itself will move.