They will continue until a physical barrier exists that prevents any chance of them crossing in between authorized points of entry.
They will continue until we abandon our outdated and self-destructive concepts of "asylum", and permit next-to-no admittance for such nonsense.
They will continue until we (as a nation) come to the realization that "immigration" of ANY kind is no longer needed to sustain America's well-being. With 300+ million, we are "full up". We don't need any more.