Step 1: Define the lesion. Low radial nerve palsy means injury to the deep branch of the radial nerve, the posterior interosseous nerve (PIN), distal to the elbow after the radial nerve has divided into superficial and deep branches.
Step 2: Identify what is supplied above this level. The extensor carpi radialis longus (ECRL) is supplied by the radial nerve proper before it divides, so its fibres branch off proximal to the PIN. Therefore in a low (PIN) lesion the ECRL is spared.
Step 3: Identify what is supplied by the PIN. The PIN supplies the extensor carpi radialis brevis, the finger and thumb extensors (extensor digitorum, extensor indicis, extensor digiti minimi, abductor pollicis longus, extensor pollicis longus and brevis), and the supinator. These are all weakened in a low lesion.
Step 4: Sensation. The PIN is essentially a motor nerve, and cutaneous sensation of the dorsum of the hand is carried by the superficial radial nerve, which also branches off proximally. Thus sensation is preserved, and finger drop occurs without true complete wrist drop because the ECRL still works.
Step 5: Pick the exception. The stem asks which structure is NOT affected. Since the ECRL is supplied above the lesion, it is the exception.
Hence the correct answer is option A, Extensor carpi radialis longus.