Why are people unemployed? Those business plans are illegal that would make hiring them profitable. In some cases there are solid laws against particular business plans; in others the accumulation of goofy regulation has made nominally legal business plans unprofitable. But the people are still here.
In the absence of welfare, it wouldn’t be possible (in the long run) to pay a worker less than a living wage. He wouldn’t live, and then there would be no worker. Before he even starved, he wouldn’t be able to buy gas to get to work. Before that, the lender would repossess his car. Welfare makes viable some business plans that rely on paying workers less than a living wage.
Similarly, it’s not so much that immigrants take jobs. For some time now there haven’t been “jobs” as fixed things. There are business plans (and they aren’t fixed.)
The workers available are one limitation on what business plans are viable. Maybe industrial-scale poultry production is only possible if a large number of recent immigrants are available to cut up chickens in the factory. Maybe some business plans only make sense if you can have a bunch of special visa holders living in a dorm and being bused in to their cubicles every morning.
So it’s not that immigrants take jobs. It’s that constant unrestricted immigration, and the assumption that it will continue forever, affect what business plans are viable.