You ask the question "where is the rest of the family" but spend not a second considering some likely answers ? I guess you're assuming they just don't care ?  It suits you to assume the worst because nothing suits conservatives more than to always assume the poor are poor because of bad decisions or irresponsible behavior - despite overwhelming proof that this is not, almost ever, the case.

Just some of the likely options: they are dead, perhaps the child's mother was just another victim of our high murder-rate, perhaps she died from disease and our inability to provide quality healthcare to all. Perhaps she is in prison for some minor drug offense that harmed nobody else. 

You're not witnessing a lack of familial responsibility. The facts we have is proof OF that very responsibility. A grandmother raising her grandchildren despite her own poverty - suggests that there was nobody else to raise them, but she stepped up and is doing so.

Trust the poor, not the rich.