Nothing presents a greater problem to plants and therefore to gardeners than dry shade.
All green plants need sunlight and water to survive, without which they are unlikely to thrive. We must not despair because the adaptability of certain plants and the diversification of the plant kingdom during their evolution is amazing.
Look at the site, find out what is causing the shade. Is it walls or trees? Are they deciduous or conifers? Once you have identified the problem and its severity, you are able to deal with it. All you need do is select the right plants making the growing conditions as favourable as possible.
If the shade is caused by deciduous trees, go for early flowering plants which mature before the leaf canopy develops. Most woodland species are like that including winter Hellebores, late spring bulbs and perennials. Woodland species tolerate dry shade as long as they have been watered well during flowering time. Hellebores and Bergenias provide permanent greenness with seasonal highlights of colour. So do some ferns including the hart's tongue and the soft shield fern. These are both drought tolerant and evergreen.
There are plenty of dark-leaved evergreens which love dry shade, such as butcher's broom, On their own, they would be very dull but highlighted with a selection of pale flowers, bulbs or contrasted with variegated foliage they will be perfect.
Plants tolerate dry shade in two ways. Growth either speeds up or slows down. Woodland species like bluebells, primroses and oxlips grow rapidly in spring, flowering and setting seed before the woodland canopy has thickened. Others like Hellebores, Brunnera and Solomon's seal , erupt into growth early and then after flowering quietly, their seed slowly ripens in summer. Some plants like ivy, laurels and evergreen ferns have foliage which is soft when young but becomes thick and leathery with age. This reduces water loss.
Space is running out, so a bedtime reading of dry shade in a gardening book will help further with the 'impossible site'.