I don't see how that situation changes after Brexit for current illegals. Currently any illegal migrants in Ireland can cross unhindered into Northern Ireland, and after Brexit that situation won't change.
If we decide to make new laws making immigration illegal for certain categories of EU citizens (and that's a big if) then it's true that those illegal immigrants belonging to that new category will also be able to cross unhindered.
The trick (this applies to all illegals) is to try to catch them when they attempt to spend money by a card, or buy or rent somewhere to live, or become employed, or any of the other numerous things that everyone does where identity is checked.