In a 1- to 2-quart pan over medium-high heat, boil vinegar until slightly syrupy and reduced to about 1/3 cup, about 6 minutes. Let cool to room temperature, 5 to 10 minutes.
Meanwhile, rinse salmon and pat dry. Sprinkle with salt and pepper.
Rinse fig leaves and pat dry. Lay dark side down, stem end pointing toward you. Break center vein of leaf close to stem so leaf will fold easily. Generously brush top of leaf with reduced vinegar.
Place one piece of salmon horizontally across middle of leaf. If salmon has a thin end, tuck under so the piece is evenly thick. Brush salmon with reduced vinegar. Fold stem end of leaf over salmon. Fold in sides, then roll up to enclose fish (if leaf is not large enough to wrap around fish, unfold and lay a second leaf slightly overlapping the first; use both leaves to wrap fish). Dampen a 12-inch length of heavy cotton string and wrap around center of bundle, then turn 90° and wrap in the other direction; tie securely, then trim string ends 1/2 inch from knot. Repeat to wrap remaining salmon. Brush outsides of bundles with olive oil.
Lay bundles on an oiled grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid on gas grill. Cook, turning once, until a thermometer inserted through leaf into center of fish reaches 140°, 8 to 10 minutes total. With a wide spatula, transfer each bundle to a dinner plate. Cut string and serve with fig skewers; unwrap bundles and discard fig leaves before eating.
Fig skewers. Soak 8 wood skewers (at least 8 in. long) in cold water for about 10 minutes. Rinse 16 firm-ripe figs and pat dry. Trim away stem ends; cut figs in half lengthwise. Thread 4 fig halves onto each skewer. Drizzle cut sides with a total of 2 tablespoons lime juice and sprinkle with about 1/4 teaspoon salt. Grill figs cut side down over high heat until warm and slightly charred, about 2 minutes. Makes 4 servings.