Which structure consists of dense fibers that support a tooth in its socket?

The periodontal ligament is the correct answer because it is specifically designed to anchor the tooth firmly within its socket in the jawbone. This structure consists of dense connective tissue fibers that connect the cementum of the tooth root to the alveolar bone, providing both stability and support. The fibers within the periodontal ligament help absorb the forces exerted during chewing and maintain the position of the tooth.

The alveolus refers to the bony socket that houses the tooth, while dentin is the hard tissue that makes up the majority of the tooth's structure beneath the enamel. Cementum is a calcified substance covering the tooth root, which aids in anchoring the periodontal ligament fibers but does not provide the direct supportive function that the periodontal ligament does. Therefore, the specific role of the periodontal ligament in maintaining tooth stability makes it the correct choice for this question.