Unfortunately, often times nothing happens. Employers routinely fail to enforce their agreements in favor of saving money. However, in theory, the remedies for a breach of contract are written right into the contract itself. This is also the case for non-disclosure agreements (NDAs).
One thing I’ve noticed over the years are NDAs with vague or broad language about what information is confidential. It’s important to include details in your NDA on what is covered by the contract, as well as the repercussions for disclosing such information. In almost all cases involving an NDA breach, you'll be able to pursue damages stemming from a breach of contract. Other legal recourses may include copyright infringement, trade secret misappropriation, breach of fiduciary duty, conversion, and other various IP violations.
Many of the laws across the country that protect trade secrets and confidential commercial information are based upon the Uniform Trade Secrets Act. Information protected by these laws includes patterns, formulas, drawings, devices, programs and codes, processes and techniques. Some states and jurisdictions also include customer lists as trade secrets.