Can cavities migrate to the root?

Cavity migration: Yes, that would be an abscess to the tooth.

Sort of-: Dental caries is the result of bacteria settling onto teeth and metabolizing the foods you eat. The end product of that metabolism is acid. The acid demineralizes tooth structure. This can start on crown of the tooth- the enamel, or the root. Unchecked, the demineralization can continue inside the tooth, destroying the tooth. Eventually getting to the tooth's nerve, requiring a root canal.

Yes root caries.: In children and young adults cavities go through the enamel and into the dentin. As adults the roots can become exposed and when decay occurs it can destroy the root very rapidly. When the decay extends into the nerve a root canal maybe necessary or the tooth may have to be extracted.

Yes. Two ways: A cavity can 'attack' the root surface of a tooth. If a cavity becomes large enough to reach the nerve of a tooth, it can kill the nerve of a tooth inside of the root.