Number one question asked "why does concrete crack"
There is many different types of concrete cracks.
If cracks appear shortly after placement (12 hour to 36 hours) they are considered "drying cracks" (although concrete does not "dry" the hardening is a chemical reaction). This happens because the mix water is evaporating and hence creating less volume in the concrete creating cracks. These cracks are using only surface cracks and are using filled with paste during power troweling. They can reappear later but are only super fiscal and pose limited to no concern for epoxy or cement based topping coats.
If they appear 36 hours to 28 days later usually this is plastic shrinkage cracks (caused by chemical reaction in the concrete along with evaporation of mix water). Typically saw cuts are used to create a controlled and visually pleasing crack. (ensure saw cuts are 1/3 depth of slab). If you would rather not saw cut there are ways to reduce your risk of cracking for a typical garage floor (20X24). WET CURE, nothing is better for concrete then to be flooded and keep wet for at least 7 days. When we do bridge decks we wet cure until full design strength is reached (28 days to 56 days) same with ice rinks.
NOW what you are dealing with is not a concrete issue at all. Your sub base was not compacted correctly and you sir have sub base failure. Is this a big concern, short answer NO your house is not going to fall down (unless your footings move highly unlikely). If this was a warehouse with automated fork lifts then this would be a disaster.
Option one remove slab. My preferred method is to use a gas walk behind saw and cut the slab out by pieces. I just hate the jack hammer and the walk behind is very easy to use. Rental rates will dictate your method. Rent a large compactor and cycle 3 times between wet and dry compacting. Put down welded wire mess but also use pyramids or bricks to hold the mesh off the ground and in the middle of the slab. NOW for the trick. Call up your local Ready Mix supplier and ask for Self Consolidating concrete (I work for Lafarge and we offer a product called Agilia (R) youtube it pretty unreal stuff). Follow the directions and pour it. You will be very happy with the finished product.
Option 2 top the floor for levelness and then cover with rubber tiles, carpet, etc (I would stay away from any mortar based tiles as the floor is still going to move and the cracks will come though the tiles). The concrete will still crack and you have not solved the main issue but it is a very viable low cost low effort option.
Option 3 (Which one of my customers recently did) removed only the area that had sunken. Compacted the subbase, drilled dowels into the existing slab and used 14mm rebar tied together at 16 inches. He order 35mpa concrete with poly fiber and re poured area. Wet cured for 7 days. He then rented a floor grinder and smoother out the entire floor. Followed by decorative saw cutting and acid staining. Came out really nice. Only time will tell how long it lasts but for then next 10 years it will be great.
Once again consult your local concrete supplier. Ask what they suggest and