## Core Concept
The question pertains to a degenerative disorder affecting the deeper structures of one side of the face, including fat, muscle, cartilage, and bone. This condition is characterized by atrophic changes leading to facial asymmetry. The disorder in question is likely related to conditions that cause hemiatrophy or localized atrophy of facial tissues.

## Why the Correct Answer is Right
The correct answer, **Hemifacial Atrophy (Romberg's disease)**, is a rare degenerative disorder characterized by progressive atrophy of the skin and subcutaneous tissues of one side of the face. This condition can lead to significant disfigurement as it affects not just the skin but also the underlying fat, muscle, cartilage, and bone, leading to a sunken appearance on the affected side of the face. The exact cause of Romberg's disease is unknown, but it is believed to be related to autoimmune or neurogenic factors.

## Why Each Wrong Option is Incorrect
- **Option A:** This option is not specified, but based on the context, any condition not matching the description of Romberg's disease or hemifacial atrophy would be incorrect.
- **Option B:** Similarly, without specifics, any condition not characterized by unilateral facial atrophy involving deeper structures would not fit.
- **Option C:** This option, like A and B, lacks detail but would be incorrect if it doesn't describe a condition with similar characteristics.

## Clinical Pearl / High-Yield Fact
A key clinical pearl for this question is that Romberg's disease or hemifacial atrophy often presents with a slowly progressive atrophy that can lead to significant facial asymmetry. Early recognition is crucial for potential interventions, although treatments are often focused on cosmetic and supportive measures. A classic clinical feature is the "coup de sabre" or "saber blow" appearance on the forehead due to atrophy.

## Correct Answer: D. Hemifacial Atrophy (Romberg's disease)