1. Cut off outer peel and membrane from each fruit, following curve of fruit. Then cut between inner membranes to free segments; discard membranes. Put fruit in a clean, widemouth 1-qt. canning jar. Add enough vinegar to cover. Close jar tightly and shake vigorously for 10 seconds. Push down grapefruit until covered by vinegar so vinegar can draw out their flavor. (Keep fruit completely submerged to prevent undesirable bacteria or mold from growing on it.)
2. Cover jar with a piece of cheesecloth (so air can get in and help start fermentation) and securely attach with a rubber band or the jar ring. Leave at room temperature for about 12 hours.
3. Discard cheesecloth. Replace lid and ring, secure tightly, and repeat the vigorous shaking daily for 7 days, keeping at room temperature.
4. Pour mixture into a wide strainer set over a bowl. Set aside fruit for another use. Return liquid to jar, using a funnel. Add grapefruit juice and sugar, cover, and shake until dissolved, about 2 minutes.
5. Chill 7 days for flavors to meld, giving the bottle a vigorous shake every day to be sure sugar is dissolved. Use, or chill up to 4 months (shake before using). The shrub will get more syrupy with time.
*Find raw coconut vinegar at natural-foods stores (see a store locator at coconutsecret.com). For a bright color in the shrub, Karlin likes Trader Joe's organic evaporated cane juice sugar.
Make ahead: Up to 4 months, chilled.