Generally, the answer is no. Most policies offered by insurers exclude coverage for foundation-based issues. In the event of a foundation cracking or a house beginning to sinking a homeowner is on their own. This is not always the case as some insurers do offer that type of coverage but it is a rarity. It also has to do with the area. If you live in an area where such a hazard is common it may be written into the policy. Once again this is a rarity.
In most cases coverage for foundation-related issues is extra. It is an addition you can add to your base policy not unlike flood or fire coverage. Most often it is bundled with these two as a buyer's incentive. If you happen to have purchased additional coverage for flood or fire you may want to look at your policy. You may very well be covered in this circumstance. This is not the only loophole available however.
The first thing you need to ascertain is what is causing your slab to sink. If a hoe foundation is damaged due to another incident occurring within the home it will be covered. So if you have a major plumbing issue that ends up causing your foundation to subside it will be covered. So find out if your specific problem is linking to something your base policy would normally cover. If it is than coverage will be doctored in as it is the result of adjacent damage. Also, be sure to take a good look at your policy as you may be a rare case that has this coverage already present.