Breaking an NDA is the same as breaking any other contract. In the event of NDA's breach, the disclosing party is entitled to take legal actions against the offending party and get either monetary damage or an injunction. That's why the agreement should contain the remedies clause, which determines the costs of violating the document.
At any point, after discovering public disclosure of your confidential data, it is crucial to gather evidence against the violation of the NDA's terms as soon as possible. The injured (disclosing) party should find out who and how has leaked the information. Before filing a lawsuit, the disclosing party is required to consider whether the leaked information is being disclosed intentionally or accidentally and whether the recipient is the one who is responsible for the leak. It is also important to prove that such a leak has actually caused damage to the company.