Interesting thought. When a person comes here legally on an immigration visa, it has to be proven that they have the means to live at least at 120% of the poverty line. Do the math.
The poverty line isn't very high --- and it means the sponsor must be at 120% of the poverty line, the immigrant's worth might be 0 and the combined incomes are looked at when qualifying the immigrant for means tested programs ---ie welfare. The strategy most use --- don't have the wealthier family members do the sponsoring --- find the one with the lowest income, let them do the sponsoring, the immigrant gets all kinds of welfare. They also can use more than one family member to -- a combination of two or more --- they can be at 60% each --- combined they make 120% and the immigrant will easily qualify for all the many welfare programs.