Step 1: Match each brainstem artery to its territory. PICA, a branch of the vertebral artery, feeds the dorsolateral medulla, so its loss strikes the lateral medullary structures.
Step 2: The dorsolateral medulla houses the spinal trigeminal nucleus, the spinothalamic tract, vestibular nuclei, nucleus ambiguus and descending sympathetic fibres. Damaging all of these at once produces Wallenberg (lateral medullary) syndrome - crossed sensory loss, vertigo, bulbar signs and Horner syndrome. So PICA thrombosis equals lateral medullary syndrome.
Step 3: Eliminate the rest. Weber syndrome is a ventral midbrain stroke from posterior cerebral artery perforators. Medial medullary syndrome follows anterior spinal artery occlusion and gives contralateral hemiplegia with tongue deviation. Neither involves PICA, so 'none' is also incorrect.
\[\boxed{\text{Lateral medullary (Wallenberg) syndrome}}\]