Libertarians don't even believe in borders.
There are no illegal immifgants in their view -- can't be.
You obviously don't understand libertarianism. Libertarians are the strongest defenders of private borders, but we don't believe
(a) that the government has a right to tell you who to invite onto your property, or (b) that anyone (including a voting majority) has a right to take your money and give it to someone else. The quandary for libertarians on immigration issues is that U.S. immigration laws both tend to keep invited, productive people out of the country and do a lousy job of keeping uninvited guests out.
For example, I was told a few years ago by a photoprocessing machine vendor that he cannot find enough people in this country with the skills to service his machines and he can't import Germans who have those skills because of the bureaucratic maze that characterizes our immigration system. Hard working, highly productive people are being kept out of our country while welfare seekers who don't care about breaking laws are able to emigrate to the U.S. As long as people who call themselves "conservatives" keep electing presidents and Congresscritters who vote to continue to rob Peter to pay Paul (or Jose), this situation will continue.