Continuing erosion of the structure of low-income families perpetuates a vicious cycle of moral and economic troubles--poverty, drug and alcohol dependency, out-of-wedlock births, child and spouse abuse, juvenile delinquency, and crime--that feed on and create more impaired families. Accordingly, this report contends that the major portion of the funds expended in aid of low-income families should be earmarked for improving services to poor female-headed families, particularly those in which the mother bore children out of wedlock. Because these families are in the worst economic condition and experience disproportionately high levels of social problems, it is proposed that delivery of the myriad programs intended for these families be consolidated, with a focus on enhancing opportunities for self-sufficiency. After an introductory discussion of the eroding family and a critique of the fragmented welfare system, the report addresses the following topics: barriers to family self-sufficiency; current responses and resources; the emergence, guiding principles, governance, and future of family investment initiatives; and practical considerations for implementing the proposal, including eligibility issues, access and management, resource commitment, and political will. Appended are tables showing: (1) budgetary data for major antipoverty programs and their fiscal 1987 federal, state, and local spending; (2) antipoverty allocations by program and state for 20 programs compiled from Office of Management and Budget data; and (3) summary descriptions of the same 20 antipoverty programs. (TE)