Final answer:
The Electronic Communications Privacy Act (ECPA) of 1986 is the federal law that primarily deals with the unlawful access to stored electronic communications, often updated to address emerging cyber data and privacy issues.
Step-by-step explanation:
The federal law that primarily addresses unlawful access to stored electronic communications is known as the Electronic Communications Privacy Act (ECPA) of 1986. The ECPA was enacted to extend government restrictions on wire taps from telephone calls to include transmissions of electronic data by computer, while also adding new provisions for access, use, disclosure, interception, and privacy protections of electronic communications. The act has been updated several times to keep pace with the rapidly evolving technology and the challenges faced in cyber data and privacy issues. Moreover, the ECPA plays a crucial role alongside other laws such as the Children's Online Privacy Protection Act (COPPA) and the Patriot Act, in governing how personal data is stored and accessed, ensuring the protection against unreasonable searches and seizures under the Fourth Amendment and tackling concerns over areas like children's online safety and terrorism.