Up until the arrival of the XXth century and the housing policies, it was common to see people build their own homes, especially in villages and urban areas in which individual housing was common; homes were extended according to the household economy.
Even if this is still possible in some areas, in Europe now the usual is to see housing as a finished product to which you come to live without having been involved in the works, and without plans for a future extension, and that includes social housing (even if in somehow recent moments there were still in parts of Spain experiences of social housing involving work by future dwellers). In fact, building codes and quality demands make quite difficult the option.
How to organize a housing policy in countries with scarce public resources, low income populations and pressing needs? In Latin America it is common to see “progressive housing” programs and the Chilean has a 50 years experience. The public administration (or the future dwellers in some cases) builds a reduced part of the building, with the load bearing main elements and the most complex systems (water, sewage, energy), and later each family extends the building according to its economic capacity. It is a far cry from the idea of complete formal control of the urban image, there are many issues that are far from well solved, but this has allowed a sizeable group of households to own a place to call their own. The programs have been linked in many countries to the large land property regularization programs.
The practice Elemental (www.elementalchile.cl), led by Alejandro Aravena, has recent works that illustrate well this principle.