Hello H2K I would call it an adjective, and predicative. I would say that it functions here as an object complement. But other members may have a different view.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
Miriam
But there is more to say about "alive": it is one of the few adjectives in English (such as alone and awake) which are generally used pospositively, that is, after the noun they modify. So, in this case, I wouldn't say "alive" is an object complement. Rather, the whole noun phrase "a woman alive" is the direct object. Let's suppose that instead of burning women