If there's only two people in economic, suppose a person have a comparative advantage in one good, and he has the same productivity in another good. if two people can trade, should he always completely specialise in the good which he has comparative advantage?

I think this might be right theortically, but what if the second person produce both good and since the first person doesn't produce a good at all and he has only one good in hand, so he may be taken advantage from other?