**Core Concept**
A parotidectomy is a surgical procedure to remove part or all of the parotid gland, a major salivary gland located in the face. The complications associated with this surgery can be related to the gland's anatomy and its functions.

**Why the Correct Answer is Right**
The correct answer is a complication that is not typically associated with parotidectomy. The parotid gland is closely related to the facial nerve, which runs through the gland. Complications such as **facial nerve paralysis** (Option C) are well-documented risks of the surgery due to the close proximity of the nerve to the gland. However, the correct answer is not related to the gland's anatomy or its functions.

**Why Each Wrong Option is Incorrect**
**Option A:** Facial nerve paralysis is a known complication of parotidectomy due to the close proximity of the nerve to the gland.
**Option B:** Frey's syndrome (also known as gustatory sweating) is a complication of parotidectomy, characterized by excessive sweating and flushing of the skin in response to eating, due to aberrant regeneration of nerve fibers between the remaining parotid tissue and the overlying skin.
**Option D:** Hematoma formation is a possible complication of parotidectomy, which can be life-threatening if not promptly treated.

**Clinical Pearl / High-Yield Fact**
It is essential for surgeons to carefully identify and preserve the facial nerve during parotidectomy to avoid complications such as facial nerve paralysis.

**Correct Answer: D. Hematoma formation is a possible complication of parotidectomy, which can be life-threatening if not promptly treated.**