Underpinning is most likely the most antique method of stabilizing foundations, and even today, it can be used in many situations.
It basically involves strengthening the foundation structure by extending it until it reaches consistent layers of soil, and at the same time the contact area at the base is increased in order to decrease and distribute the unit load.
In many cases, it is the only possible solution when constructing for example floors or drainage in very old buildings where foundations are essentially absent.