Self-lubricating bullets seem to have been invented by Daniel B. Wesson, one of the founders of Smith & Wesson. He received a patent for his design in 1893. During this era, fouling in firearms was a big problem because smokeless powders hadn't been invented yet and black powder left a lot residue behind in the barrel. Excessive fouling would cause the finest revolvers in the world to become inaccurate, especially when they were shot rapidly in dry conditions.
Smith & Wesson self lubricating bullet. Click on image to enlarge. Public domain image
In the above image, we see a Smith & Wesson self-lubricating bullet. The bullet has a hollow core in its base, about 1/8th inch in diameter. Inside this core, a copper plug is inserted and the core is filled with lubricant A. The base of the core has a brass plug B. Four tiny passages C are drilled along the side of the bullet and these passages are also filled with lubricant.
Self-lubricating bullet when fired. Click on image to enlarge. Public domain image.
When the bullet is fired, the brass plug B is pushed inside the bullet by the expanding gases, thereby forcing out the lubricant out of the passages C in the conical front of the bullet. The theory was that the lubricant would distribute itself to the walls of the barrel and keep it moist. The black powder residue, which is very hot, would cool down more rapidly because of the lubricant and adhere only loosely to the barrel and could be cleaned easily with only a wire brush.
The book goes on to say that this cartridge was tested by the US Government and seemed to show more accuracy than using regular ammunition, while being slightly more expensive. Smith & Wesson used this idea for several of their cartridges, .38 S&W, .38 Special, .32 S&W, .32 S&W Long, .44 S&W Russian etc.
With the invention of more modern and cleaner burning powders, this type of bullet seems to have lost its popularity.