Most rich countries take good care of their poor. In the US, most states will pay for food, heating, sometimes even internet access, not to mention healthcare, if you are poor. Indigent children also have separate healthcare programs targeted towards them and receive free lunches at school to encourage them to concentrate on school. Furthermore, there is also Unemployment Insurance which provides for months of basic income if you become unemployed. Finally, there is disability payments. This is the situation where you are severely disabled and can't work, in which case, the government will pay you a basic income for the rest of your life. Most of these programs are well-run and disburse money efficiently.
Fraud to get disability payments is very high. People who are unable to rejoin the job market sometimes make the difficult decision to connive with sympathetic doctors to get this. But once you do this, you can never go back to work in any official capacity. This is the one case where people who are chronically unemployed give up and become wards of the state. So the 'desperately poor' are actually taken care of in some fashion in the US.
The problem is that the people who are the 'working poor' often get shafted. These are the janitors who are working all hours of the day, the baggers at the grocery store, the short order cooks, the security people who patrol industrial and residential facilities, etc. Even though their children are eligible for all the benefits above in many cases, it's still difficult to raise a family if there is one breadwinner who makes minimum wage. These people are not eligible for many benefits programs and also do not generally get healthcare from their employers (employers deliberately keep hours/week down to avoid this expense). The problem is, 'taking care' of these people is very hard: they are the majority of the workforce, and I suspect that there is not enough money to fund programs for these people because of the sheer size of this workforce. Also remember that this group oftentimes does not have powerful unions (many subgroups do), which means politicians do not have to listen to them.