Place green beans in a large saucepan with a lid. Pour water over beans to cover; stir in salt. Bring to a boil over medium heat, reduce heat to low, cover, and simmer until beans are very tender, 3 to 4 hours; add water throughout cooking as needed to keep moist.
Add potatoes and smoked sausage; cover and simmer until potatoes are very tender and beans and potatoes have absorbed the smoky flavor of sausage, about 2 more hours.
Amy's Green Beans and Sausage Dish · Dinner Match Lab | Dinner Match Lab