There are some in the libertarian movement who believe that national borders should remain closed due to the fact that many of the immigrants (at least from certain countries or economic standing) tend to end up on welfare. The argument goes like this: more immigration, more welfare. Therefore, they believe that immigration grows the state.
It is true that once someone goes on welfare, it is difficult to pull them off it. But it is not the fault of the immigrant that the welfare is being offered. The immigrant is not the source of the welfare, he is the recipient. If I left some fruit out on my kitchen counter to rot and developed a fly problem, do you blame the flies or do you blame me for leaving fruit out? I cannot control what flies do, but I can control how long I leave fruit out and thus don’t even give the flies a chance to cause problems in the first place.
I am not, of course, equating immigrants to flies if it were questionable what I meant by that analogy.
Furthermore, since the immigrant is not the one who is the source of the welfare, it is incorrect to say that immigrants are the cause of increased welfare and thus the growth of the state. Sure, there is a relation, but this is an example of confusing correlation and causation.
So who or what is the cause of the growth of the state via welfare programs? It’s the state! Who else would you expect?