Pour off any fat from skillet in which pork was cooked. Add oil and heat skillet over medium heat until shimmering. Add onion and cook, stirring occasionally, until softened and beginning to brown, 3 to 4 minutes. Increase heat to medium-high and add broth and figs; bring to simmer, scraping bottom of skillet with wooden spoon to loosen any browned bits. Simmer until liquid is reduced to 1/3 cup, 3 to 4 minutes. Add syrup, vinegar, mustard, and any juices from resting meat and cook until thickened and reduced to 1 1/4 cup, 3 to 4 minutes longer. Adjust seasonings with salt and pepper, pour sauce over pork, and serve.