**Core Concept**
Shoulder dysfunction syndrome, also known as Thoracodorsal nerve palsy or Thoracodorsal nerve injury, is a complication of radical neck dissection. It occurs due to the damage to the thoracodorsal nerve, which is a branch of the brachial plexus. The thoracodorsal nerve innervates the latissimus dorsi muscle, which is responsible for shoulder abduction and extension.

**Why the Correct Answer is Right**
The thoracodorsal nerve is at risk during radical neck dissection due to its close proximity to the surgical field. The nerve arises from the posterior cord of the brachial plexus and courses down the arm to innervate the latissimus dorsi muscle. Damage to this nerve leads to weakness or paralysis of the latissimus dorsi muscle, resulting in shoulder dysfunction syndrome. The symptoms include weakness in shoulder abduction and extension, and the patient may also experience difficulty in performing activities that require the use of the arm.

**Why Each Wrong Option is Incorrect**
* **Option A:** The long thoracic nerve is responsible for innervating the serratus anterior muscle, which is involved in shoulder adduction and rotation. Damage to this nerve leads to winged scapula syndrome, not shoulder dysfunction syndrome.
* **Option B:** The axillary nerve is a branch of the brachial plexus that innervates the deltoid and teres minor muscles. Damage to this nerve leads to weakness in shoulder abduction, but it is not directly related to radical neck dissection.
* **Option D:** The radial nerve is a branch of the brachial plexus that innervates the extensor muscles of the forearm and hand. Damage to this nerve leads to wrist drop and not shoulder dysfunction syndrome.

**Clinical Pearl / High-Yield Fact**
It is essential to identify and preserve the thoracodorsal nerve during radical neck dissection to prevent shoulder dysfunction syndrome. The surgeon should carefully dissect the nerve and avoid damaging it during the procedure.

**Correct Answer:** C.