If by "preservative" you mean an antioxidant -- something that prevents chemical oxidation of fats -- rosemary oleoresin (ROE) works very well and it's arguably about as "natural" as you can get.
If by preservative you mean a product that inhibits the growth of bacteria, fungi, and other microorganisms, it's not required in bar (NaOH) soap and concentrated liquid (KOH) soap. The alkalinity (high pH) of soap functions as the antimicrobial preservative. Which is good, because there are very few preservatives that function in the high pH of soap.
If you add large pieces of food in or on the soap (for example coarsely ground oatmeal or large pieces of vegetables), those particles can become moldy. The solution to this problem is to not do this.