The HOS theory says that a country exports the goods that are intensive in the use of the factor of production that is abundant in the country. A country with lots of workers, and according to theory cheap labor, would produce goods that are labor intensive and export them, while importing capital intensive goods. The graph below illustrates the argument.
The capital controversy showed that there is no reason, in a world with multiple capital goods, to have a monotonic decreasing relation between capital intensity and the remuneration of capital. One way in which that effect could be represented would be with a capital intensity reversal in the production of goods a and b, as shown below.
As a result it is not generally true that trade depends on comparative advantage based on relative scarcities of factors of production. This suggests (as the critique of the Ricardian version of the model) that absolute advantage, lower costs, might be more important than conventional wisdom suggests. Also, it implies that history and institutions are central to understand patterns of trade specialization.
The seminal work in this area was done by Ian Steedman, extending the ideas of Sraffa to foreign trade. The classic papers have been collected in Steedman's edited book Fundamental Issues in Trade Theory.