A boat that size would have a water maker for converting sea water and would work until diesel fuel ran out. Besides stored food, they may be successful fishing, etc. Security wise it would be easy to defend and mobile so they could travel to maybe an unaffected area.
On the down side, with the world going down, weather forecasting will become a thing of the past and will become their greatest danger. They are quite likely to encounter hostility everywhere they attempt to land. And they will run out of fuel and then they are trapped...
These are just some of the thoughts and ramblings of a crazy old sailor...