How a local crew fixes it
The inspector picks the fix based on your house, your soil and what caused the movement. These are the common methods.
Wall anchors and wall braces
When soil pushes a basement wall in, the fix is to hold it, and sometimes pull it back. Wall anchors run from the wall out into firm soil in the yard. Steel beams or carbon fiber straps brace the wall from the inside. See wall anchors for how each one works.
Stone and mortar repair
Old stone walls can often be saved. Loose mortar is raked out and packed with new mortar. This is called repointing. Badly damaged parts can be rebuilt. An inside drain often goes in at the same time to keep water off the wall.
Crack repair
Cracks in poured walls can be filled with epoxy or a foam that seals the crack all the way through. Cracks from a moving wall need bracing first, then sealing. See foundation crack repair.
Steel piers
When a corner or one side of the house sinks, steel piers go down beside the footing until they reach firm ground. Then the house is lifted and held there. Helical piers screw into the ground. They work well for lighter loads like porches and add-ons.
Fixing the water
If water caused the movement, a brace alone will not stop it from happening to the next wall. Inside drains, a sump pump, downspout extensions and regrading keep water away. See basement waterproofing.
Crawl space support
Some homes, and many add-ons like back porches and sunrooms, sit over a crawl space. Sagging floors there are fixed with new supports under the beams. See crawl space repair.