This paper expands on an earlier analysis finding that massive loss of housing to contagious urban decay in New York City, after a delay, has materially contributed to creation of a literal famine of housing and community. As in traditional food famines, a great housing deficit, some estimates suggest a quarter million unit shortfall affecting perhaps a million people, has structured itself according to the city's social hierarchy, striking most seriously the most vulnerable of the population. These increasingly become precariously housed and then, with time, homeless as the decline of low-income housing supply collides with increasing numbers of the poor. Previous simple mathematical analysis suggested the demographics of those precariously housed strongly determines the dynamics of homelessness. A generalized treatment is given here, linking the number precariously housed in New York City to contagious urban decay and time lag effects resulting from housing units made available by an episode of out-migration by the middle class, along with the impact of expected deterioration of public health causing elevated death rates among the precariously housed and the homeless. The resulting mathematical model raises the possibility of complex, counterintuitive and self reinforcing cyclic time dynamics, with deceptive apparently latent periods, and serious instabilities, perhaps capable of rapidly producing unexpected avalanches of homeless people. Suggestions are made for intervention and control, based on understanding the complex 'life cycle' of the process. These, it is found, must include prompt restoration of critical housing related municipal services, particularly fire extinguishment.