First, we do not use bad poetry added to the base of the Statue of Liberty 20 years after the fact as a fundraiser as a substitute for actual immigration law that elected representatives have voted on.
Second, every single immigrant who arrived at Ellis Island was inspected. They were not admitted if they failed health examinations, or if they did not have proof of either a financial sponsor or sufficient funds to support themselves.
Third, if the US economy reverts to a situation where masses of unskilled laborers can meaningfully contribute, and there is no welfare state that pays people for not working, you'll be the first to know.