Recoll is a desktop full-text search tool. It will search inside of documents, including nested ones. As their site puts it:

Recoll will index an MS-Word document stored as an attachment to an e-mail message inside a Thunderbird folder archived in a Zip file (and more...). It will also help you search for it with a friendly and powerful interface, and let you open a copy of a PDF at the right page with two clicks. There is little that will remain hidden on your disk.