What is the legal status of a research project on a political candidate?

First, this is an inquiry primarily about copyright law. Generally speaking, information found in the public domain is not protected and research of that information, standing alone, is likewise unprotected. The question is what someone does with that information. If someone simply compiles the information without any synthesis or analysis, it is also unprotected because it is generally a report of facts and other public data that, as I said, is neither copyrightable nor otherwise protectible under any statutory scheme. If, on the other hand, someone writes a book that reports and analyzes information found in libraries, newspapers, etc., the book may be protected by copyright because it is both a new way of expressing existing information and a new creation of the author's thoughts and analysis of that information.

In response to the specific question, it is unlikely that the research regarding the political candidate is what...

was actually sold; rather, it is my guess that someone sold a service that included research, and perhaps conclusions based on that research. To the extent that the report of the research is protectible under our copyright laws, the inquirer is generally correct that anything produced as part of his/her duties for an employer in the ordinary course of that employment is likely to belong to the employer. The gray area begins where someone creates something for the employer that they were not hired to create or compensated for creating, in which case the product may belong to the employee.

The question about trade secrets suggests a slightly different analysis. Trade secrets are typically proprietary information or creations that are not necessarily protected or protectible under a statute but are nonetheless sensitive and important to a company's business. Such information is generally protected by nondisclosure or confidentiality agreements. In the world of politics on a grander scale, it is possible that a political polling or consulting firm will be bound by such an agreement, in which case neither the firm nor its employees may use the information that it gathers on behalf of the client except in the course of advising the client. In many instances, such agreements in the political world are unnecessary because the polling and consulting firms know that the first time they leak or use such information for purposes other than those that benefit the candidate/client will be the death-knell for that firm.