Social Darwinists were (and are) generally opposed to government aid to anyone, indeed to aid to anyone, at least any aid that is not paid for and in the direct self-interest of the person providing it. They opposed welfare, social insurance, foreign aid, and even public infrastructure.
Based (loosely) on Darwin's theory of evolution by natural selection, Social Darwinists argued that the way to achieve the best outcome in any system, be it biological, economic, or social, is to simply let all the different agents fiercely compete with one another, a constant war of all against all, and to the victor go the spoils. They theorized that this would ensure that the ones who win---and therefore the genes and individuals that survive---would be the best and the strongest.
They also believed that any attempt to intervene in that competition would ultimately be harmful; by helping those who would otherwise fail or handicapping those who would otherwise succeed, intervention in the natural state of competition would only allow the weak and inferior to prosper.
Today we know that this is not at all what evolutionary theory actually implies. Indeed, one of the central reasons why humans are so successful is that we cooperate with one another, forgoing our own narrow self-interest for the good of our tribe, our culture, our nation. Cooperative behavior is common across many species, and particularly among intelligent social species such as ourselves. Social Darwinists believed that they were applying evolution to understand human nature, but in fact they were distorting evolution and fighting human nature.