Every foundation has cracks in it! So, if you see cracks, do not jump to the conclusion that your slab is failing. When concrete cures, that is as it hardens, it shrinks a small amount. The shrinking can cause cracks of various sizes. Such cracks are called shrinkage cracks and are usually less than 1/16th of an inch wide. There is no need to worry about shrinkage cracks.
When cracks get wider than 1/16th of an inch, they are often being caused by the slab bending. The standard thickness for a slab in the DFW area is 4 inches. If you see a crack that is 1/8th of an inch wide, it almost certainly goes all the way through to the bottom of your slab. There is no need to worry about bugs or water coming up through your slab because code requires that slabs have a plastic moisture barrier under each foundation. And do not worry about your slab being pulled into pieces. The reinforcing steel will hold it together.
The best way to deal with a slab crack is to relieve the stress that caused it. If a slab crack was caused by your foundation settling, then the best repair is to lift the foundation back up and in so doing, take the stress off of the slab.
Cracks rarely close up. Bits of sand, rock and concrete will prevent a crack from closing when a foundation is lifted. If, after your foundation is lifted, you want a crack sealed, the best way is to epoxy inject the crack. Epoxy can be applied from the surface. Epoxy will not restore the original strength of your foundation but is will seal the crack with a tough material.
When cracks get really big, say an inch wide. You need to have an engineer or contractor look at your foundation. Really wide cracks mean that the foundation is unenforced, that the reinforcing failed, and that there is some very serious movement going on.
The widest cracks that I have ever seen were in Trophy Club, Texas. Trophy Club is located in Denton County north of Fort Worth and Keller. The homes in question had cracks that eventually grew to be a foot wide. In the end the homes were all torn down. What caused the disaster? The homes were built on a hillside that was sliding down onto a golf course.