Some plants can be propagated from a section of a root. Root cuttings of woody plants are usually taken from plants during the dormant season, when carbohydrate levels are high. Root cuttings of some species produce new shoots, which then form their own root system, whereas root cuttings of other plants develop root systems before producing new shoots. Examples of plants that can be propagated from root cuttings include raspberry, blackberry, rose, trumpet vine, phlox, crabapple, fig, lilac, and sumac.
Plants with large roots are normally propagated outdoors. The root cuttings should be 2 to 6 inches long. Make a straight cut on the proximal end (nearest the crown of the parent plant) and a slanted cut on the distal end (furthest from the crown) of each root cutting. Tie the cuttings in bundles with all the same type ends together. It is important to maintain the correct polarity of the cuttings. Store for 3 weeks in moist sawdust, peat moss, or sand at 40°F. Remove from storage. Space the cuttings about 2 to 3 inches apart in well-prepared garden soil. The tops of the cuttings (proximal ends) should be 2 to 3 inches below the soil surface.
For plants with small roots, cut the roots into 1 to 2 inch sections. Lay the cuttings horizontally on the medium surface in a flat and cover with about 1⁄2 inch of soil or sand. Place the flat inside a plastic bag or cover with a pane of glass. Place the flat in the shade and remove the protective cover after new shoots appear.
Here is an article that can give you additional information on several ways to propagate figs, as well as other information on growing figs..