It is very tricky indeed this question. I am very torn between radically different positions on this issue. On the one hand I belive it is very hard to argue against the argument that free migration have the potential to change alot of peoples life for the better. Even restricted forms of immigration from underdeveloped countries impose coasts on the citizens allready living in a rich country and paying taxes. Free migration after the removal of the welfare state should, however, be beneficial for both the immigrants and the citizens of the country where to they migrate. A state without a welfare system would have a natural barrier against seekers of welfare benefits. Only those beliving themselfes capable of getting some sort of employment and improving their lot would migrate to such a country.
On the other hand this means the welfare state have to be dissolved all together. And, as all libertarians know, this seems to be a goal that is impossible to achieve. As long as one lives in a society with a welfare state I think it is very hard to declare support for free immigration. The practical result of supporting such a policy is to impose on one-self an ever greater tax burden and offering non-contributors part in the welfare pie so that you also get ever smaller slices of this pie yourself.
Off course not all immigrants impose coasts on a society even when the society in question is a welfare state. People with large amounts of capital or people that are highly skilled will contribute to the economic development even in such a situation. Than there is the question about equality. People seem to choose to live among people on the same socio-economic level as themselves. I think this is because only that way can people relate and interact with eachother in the private sphere without there arising any feelings of inferiority or supremacy. You can have the best relationships with people that you share economical and educational background with. No antagonistic feelings of hatred does arise under such circumstances.
In countries where there are great differences between rich and poor different social classes seem to live very separate lifes and often seems to feel hatred towards eachother. But somehow the life inside a welfare state is hypocritical. Because the welfare state reduces the freedom of movement for poor people it is only an illusion that these are more compassionate states than the night watchmen state. In a night watchmen state you may be exposed to more sights of poverty than inside the welfare state. But the welfare state actually imposes more poverty overall than a night watchmen state. It is just that the inhabitants of the welfare state have the luxury to not see this poverty. And, over the long run, a state with minimal taxlevels and freedom of choice should improve everyones standard of life faster and more effective than any welfare state can.
But than there is the problem Porphyrogenitus mentions. If you allow very poor people to immigrate to a rich country and that country is a democracy you almost certainly will see the rise of political parties with an socialist outlook. So in that situation you will destroy freedom and impose on yourself a welfare state if you support free immigration.
It would be interesting to hear the differing opinion. I would like to hear what counter arguments libertarians in favour of an open bordes policy have to say on this issue. How is it possible to preserve freedom and stop the rise of socialist parties in a situation where very poor people are allowed to immigrate to a rich country?