I think it is about responsibility of the governments to make sure that everybody has at least minimum income security allowing life in dignity, which is a necessary condition (sometimes not sufficient) to create food security and affordable to all access to health care and other basic social services. They ways to provide such guarantees are multiple - for those able to work it is mainly through creation of quality employment opportunities, for those unable to work for various reason - through social protection systems.
See ILO Recommendation concerning national floors of social protection and the latest special issue of the International Social Security Review devoted to it.
I would say that the right to feed oneself should stand first, which however also puts responsibility on governments to fulfil this right, to protect it and to promote it. This can then mean to provide food to people who cannot feed themselves. This can be done through subsidized food or through Work for Food programs especially in the case of non-working poor. Much better would be to assure that people are paid properly so that a life in dignity becomes possible.