Sulfuric Acid liquid has a density of 1.84 g/mL. If I take a rubber stopper, which has a density of 1.10 g/mL and drop it into the acid, the rubber stopper would do this in the acid.
What we will observe is known as vulcanization. It is process by which rubber is made, more accurately, the process by which we make tyres. It was discovered by Charles Goodyear. When, sulfuric acid is added to rubber (or rubber is added to sulfuric acid), the sulfur in the acid attaches itself to the polymer chains within the rubber. This causes bridging of these various polymeric chains and a crosslinked polymeric structure is obtained. This reaction results in a thermally resistant and chemically stable compound. This means that the resulting rubber will be stiff and hard and will not melt as it warms up. This property is especially relevant for making vehicle tires, as they heat up during the operation of vehicle and ideal material should be thermally resistant, which vulcanized rubber is.
Hope this helps.