Trim fat from pork roast. Combine salt, fennel seed, tarragon, pepper and garlic in a small bowl; rub onto pork roast. Brown roast on all sides in hot oil in an extra-large skillet. Drain off fat.
Place sweet potatoes in a 6-quart slow cooker. Place roast on sweet potatoes. Add sausage. Pour the 1 can of broth and the 1/3 cup apricot nectar over all.
Cover; cook on low-heat setting for 7 to 9 hours or on high heat setting for 3-1/2 to 4-1/2 hours, adding dried apricots during the last 30 minutes of cooking.
Transfer pork, sausage, and apricots to a serving platter using a slotted spoon. Transfer sweet potato chunks to a large bowl using the slotted spoon; mash with a potato masher.
Strain cooking liquid into a glass measure cup; skim fat from cooking liquid. Measure 2 cups cooking liquid (if necessary, add enough of the additional chicken broth to equal 2 cups). Pour liquid into a medium saucepan. Combine the 1/4 cup apricot nectar and cornstarch using a wire whisk; stir into juices in saucepan. Cook and stir over medium heat until thickened and bubbly. Cook and stir for 2 minutes more. Serve pork and mashed sweet potatoes with sauce. Makes 8 servings.