Always save poultry pan drippings. Just a small amount of the rich "jus" lends a complex, savory flavor to nearly any dish (pasta, soup, or whole grains). Here, it adds depth to the fig sauce served with the chicken.
Heat oven to 300 degrees. Place chicken on a baking sheet and gently peel back skin from chicken pieces without detaching it completely. Heat until the meat is warm and the skin is crisp, about 10 minutes. Meanwhile, combine polenta and water in a medium pot over medium-high heat. Break up polenta with a wooden spoon, then stir continuously until creamy and heated through. Season with salt, spoon onto serving plates, and top with chicken.
In a small pot, combine chicken "jus," figs, and fig syrup; whisk until combined. Reduce slightly over medium-low heat. Season with pepper.Pour over chicken. Garnish with parsley.