In a 2- to 3-quart pan over medium-high heat, stir sugar, water, and corn syrup until sugar has dissolved and mixture comes to a boil, 2 to 3 minutes. Increase heat to high and boil without stirring until syrup is a deep amber color, 10 to 12 minutes longer. Remove from heat and immediately stir in whipping cream (mixture will foam). When foaming subsides, stir in coffee and salt. Let cool before using, or cover and chill up to 2 weeks (stir before using).