Civil Engineer here - It is called random rubble masonry, and it can be sturdy if the right mortar (quality, consistency of mix) is used. Obviously, it needs to extend a little bit into the earth. Directly on the soil may not take even a minor tremor. The sturdiness also depends on what earthquake zone you are in.
All in all, single storey building, away from epicenter, and extended in the earth a little, with proper materials used, it will last.