**Core Concept**
Froment's sign is a clinical indicator of ulnar nerve injury, which affects the function of the hand, particularly the adductor pollicis muscle.

**Why the Correct Answer is Right**
Froment's sign is a result of the ulnar nerve's inability to innervate the adductor pollicis muscle, leading to a compensatory action by the flexor pollicis longus muscle. This compensation causes the patient to flex the distal phalanx of the thumb as they attempt to adduct the thumb against resistance. The ulnar nerve injury affects the nerve supply to the hand, specifically the palmar interossei and the adductor pollicis muscles.

**Why Each Wrong Option is Incorrect**
**Option A:** Radial nerve injury is incorrect because it primarily affects the extension of the wrist and fingers, not the adduction of the thumb.
**Option B:** Median nerve injury is incorrect because it affects the flexion of the thumb, index, and middle fingers, but not the adduction of the thumb.
**Option C:** Posterior interosseous nerve injury is incorrect because it affects the extension of the wrist and fingers, but not the adduction of the thumb.

**Clinical Pearl / High-Yield Fact**
Froment's sign is a useful clinical indicator of ulnar nerve injury, which can occur due to various causes, including fractures, dislocations, and compression of the nerve.

**Correct Answer:** C.