IIRC Hatteras has a boat that is marginally stable with near-empty tanks. Some vessels add water as the fuel is consumed. They have really good water seperators too:
As a vessel consumes fuel, air displaces the fuel in its fuel tanks, thus reducing the
vessel’s stability. There is an added detrimental effect to stability when a tank is partially full
and the liquid inside can slosh around. The degree to which these factors affect ship stability are
dependent on ship design and the sea state. Some classes of ships are more susceptible to
stability problems than others and certain locations have historically high wave action. When
ship stability is threatened, ballast water can be pumped into a fuel tank to replace the consumed
fuel and to regain stability. Ballast water is discharged when it is no longer needed for
operational reasons or when preparing for fuel reintroduction.
To maintain safe stability, vessels without clean ballast systems may begin ballasting fuel
tanks when remaining ship’s fuel drops to approximately 70-80% of total capacity. These
vessels may continue to ballast fuel tanks until approximately 20% of ship’s fuel capacity
remains (the minimum percentage allowed by U.S. Coast Guard (USCG) ships).1 Therefore, by
the end of a voyage, as much as 80% of the fuel tanks’ contents could be seawater.
Procedures have been established for both ballasting and deballasting to minimize the
concentration of fuel in the dirty ballast.