By making immigration-without-visas a criminal offense, rather than an administrative one, the anti-immigration movement serves to drive immigrants (but not immigration) underground and makes their labor cheaper.
It's a lot like prostitution: since prostitution is a criminal offense, all prostitutes are criminals. They can be abused freely because they cannot go to the authorities without certainty being punished themselves.
By the same token, an undocumented immigrant cannot contact authorities to report they're underpaid, stolen from, beaten, imprisoned, or enslaved. (These are all things that happen regularly.) Their "criminal" status is used as a cudgel to abuse them.
Keep in mind, these are all people that just want to work in exchange for money, and they're responding to people and companies that want to hire their services. The "illegal immigration" posturing is just the buyers' way of artificially depressing prices.