When connected to an adjective, -хэн (-хан, -хон, -хөн) suffix slightly enforces the meaning of the adjective. For example, жижигхэн is slightly smaller than жижиг, but larger than маш жижиг. But a lot of people would say there is no difference when you add -хэн. So яльгүй and яльгүйхэн are almost the same meaning.