Rothbard supported open borders but was against welfare.
Rothbard was to the Right of Reagan on immigration.
http://www.lewrockwell.com/woods/woods7.html Hoppe argues that the traditional libertarian position on immigration – that is, completely open borders – is fundamentally wrongheaded, even from a libertarian point of view. Here Hoppe builds upon the late Murray Rothbard’s overhaul of the libertarian position in the early 1990s. (Rothbard, as some readers are doubtless aware, was the culturally conservative libertarian theorist who made many enemies – and at least as many new friends – when he supported Pat Buchanan in 1992.) "I began to rethink my views on immigration," Rothbard explained, "when, as the Soviet Union collapsed, it became clear that ethnic Russians had been encouraged to flood into Estonia and Latvia in order to destroy the cultures and languages of these peoples." After serious reflection, he realized that "the regime of open borders that exists de facto in the U.S. really amounts to a compulsory opening by the central state, the state in charge of all streets and public land areas, and does not genuinely reflect the wishes of the proprietors."