Combine prunes and water in a small saucepan over medium-high heat. Bring to a boil, reduce heat to low, and simmer until prunes are tender, about 5 minutes.
Drain and set aside.
Preheat oven to 350 degrees F (175 degrees C). Grease and flour a fluted tube pan (such as a Bundt®).
Mix flour, 1 1/2 cups sugar, allspice, baking soda, nutmeg, cinnamon, and salt together in a mixing bowl.
Combine vegetable oil, 1 cup buttermilk, and eggs in a separate bowl; pour them into the flour mixture.
Mix until fully incorporated. Use an electric mixer to blend in the drained prunes; the mixer will break them up a bit. Stir in the chopped pecans.
Pour batter into prepared pan and bake in preheated oven until a tester comes out clean, about 45 minutes.
Remove cake from oven and allow it to cool for at least 10 minutes on a wire rack.
To make icing, combine 1 cup sugar, margarine, 1/2 cup buttermilk, vanilla extract, and corn syrup in a saucepan and bring it to a boil over medium-high heat. Boil for a full 5 minutes, stirring occasionally.
Invert cake onto a platter and pour hot icing over the cake.
