Dry shade means different things in different regions, and plants adapt to it differently depending on what causes it. In most cases, it’s a result of unequal competition between trees and herbaceous plants: trees, with their large and extensive root systems, are more efficient at harvesting water than more shallowly-rooted plants. This competition is especially intense when the shade trees are themselves shallowly-rooted, like oaks: their roots compete directly with smaller plants growing beneath them, and because of their size, they usually win.
Dry shade can also be found in ecosystems with intense seasonal water limitation. The pine forests that grow along the Mediterranean are moist enough to support understory plants in the winter, but not in the summer. Plants in this region have developed some ingenious strategies for exploiting this seasonality: cyclamens, for example, simply go dormant in the summer to avoid competing for water, and grow and bloom in the fall and winter.