How to deal with soil erosion under slab floor of garage?
It doesn't look to me like the slab has shifted, since the crack appears level and isn't terribly wide.  I would contact a concrete contractor, one that specializes in repairs, if there is erosion under the slab they can usually pump a slurry under it to fill in the void. Is your garage floor "Floating"? Look around the edges, if the floor goes under the walls, it's part of the support of the building and you want to consult a professional immediately. If the floor butts up against the wall, it's a "floating" floor and isn't part of the structure, however you may still have erosion under the wall footing, and I would still consult a professional, however a floating floor will be easier for a contractor to break up, install proper drains and such so it won't erode underneath again, and re-pour.

You could get an endoscopic USB camera from Amazon for about $20 that you could probably snake under the slab and inspect it, but I would consult a professional. Most of these types of things are cheap to fix now, but could end up costing thousands to fix later.