It's been that way for decades. The most common method is to overstay a valid visa. Others cross the border, use rafts/boats to come by sea (no border wall), apply for asylum and then disappear. It has always been so, and will always be so until the US is no longer attractive to them (i.e. "better life"). Republican administrations, Democrat administrations...it's omnipresent.

The ONLY way to slow it down is to go after employers. If illegal immigrants can't get jobs because employers require paperwork (or they get severe penalties), then they'll mostly stop coming. But right now it's "oops, I didn't know"...the migrant gets deported, and the employer gets a slap on the wrist (if that much). But Republicans don't seem to like that solution. They just want to build 20' walls, garrison troops there, etc. Didn't work for China (i.e. the Great Wall was a failure), and it won't work now.

You have to eliminate the demand, and fining employers is the way to do it. Or at least a way to do it.