There are multiple additives that stop oil leaks. Several companies, including Bar's Leaks, STP, Lucas and PermaTech, manufacture this type of product to be added to engine oil.
Worn engine seals and gaskets cause engine oil to leak. Oil additives that claim to stop engine oil leaks work by revitalizing these seals and gaskets. The additive mixture contains chemicals that restore moisture to dry seals, making them pliable in order to properly maintain the oil pressure in the engine. In general, one bottle of additive mixes with the engine oil to restore the seal and stop the leak. Some brands allow a second application if the first one fails.