**Core Concept**
Brown-Séquard syndrome is a neurological condition resulting from a hemisection of the spinal cord, typically due to a traumatic injury. This condition leads to a characteristic pattern of sensory and motor deficits on the ipsilateral side of the lesion.

**Why the Correct Answer is Right**
The key feature of Brown-Séquard syndrome is the loss of corticospinal tract function on the ipsilateral side, resulting in weakness or paralysis of the muscles below the level of the lesion. This is due to the degeneration of the corticospinal tract, which carries motor signals from the brain to the spinal cord and ultimately to the muscles. The loss of ipsilateral proprioception (position sense) and vibration sense is also a hallmark of this condition, as these modalities are transmitted via the posterior columns of the spinal cord.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the loss of modality on the contralateral side is characteristic of central cord syndrome, not Brown-Séquard syndrome.
**Option B:** This option is incorrect because the loss of modality on the ipsilateral side is the defining feature of Brown-Séquard syndrome.
**Option C:** This option is incorrect because the loss of modality on the bilateral side is characteristic of spinal shock, not Brown-Séquard syndrome.

**Clinical Pearl / High-Yield Fact**
Brown-Séquard syndrome is often remembered using the mnemonic "CARES": Corticospinal tract (A) affected on the ipsilateral side, leading to weakness or paralysis; loss of (R)eproception and (E)sthesia (vibration sense); and (S)ensory level ( dermatomal level) typically below the lesion.

**Correct Answer:** C. Proprioception and vibration sense.