The "right of sustenance" you're describing would be more properly described not as a right of the serf, but rather a responsibility of the leige. Noblesse oblige.
If I claim to in some sense own or control another person, I become to a degree responsible for their well being. Quid pro quo.
Once they leave my service I have no further responsibility to them. In a feudal system, if the serf leaves the land, my land, my responsibility for their well-being ends and they are on their own. They are "out laws", outside the system, bound to none but provided for by none as well.
After slavery and the feudal system went away the "right to sustenance" by definition went away as well as there were no more nobles to be directly oblige'd.
A government of free men has no responsibility to care for its citizenry, merely to provide a system where they are not impeded by said government or the criminal actions of others in caring for themselves.
The "safety net", orphanages, homes for invalids or the aged, soup kitchens and the like, is to be provided by willing private members of the society, whether family or voluntary charitable organizations. A society founded on Western moral structures would have those services provided or funded privately by the wealthy who retain a certain sense of noblesse oblige to the less fortunate in general.
