There is a long standing debate in the United States about undocumented workers, and a more recent one in Europe as well. The debate is on two fronts: the public services they receive without paying taxes (in most cases), and the jobs they take away from local and the resulting pressure on local wages. In the second case, an easy solution would be for firms to stop hiring undocumented workers. But the incentives are not aligned for that, unless one puts prohibitive fines on firms doing illegal hiring.
Indeed, David Brown, Julie Hotchkiss and Myriam Quispe-Agnoli find, using administrative data from Georgia, that such firms have a competitive advantage over those the do not hire undocumented workers, or fewer. This advantage translates into a much higher survival rate, especially for little diversified firms requiring low-skilled workers. This looks like a prisoner's dilemma: if your competitor hires illegals, you have to as well, and vice-versa. But you would both be better off without, as there are legal ramifications.
Maybe those legal ramifications need to be trumped up. Indeed, the advantage of hiring illegals is often that they are willing to undercut minimum wages or various benefits legal workers have rights to. One way to avoid this this is to give illegal workers the same rights as legal workers, as I have argued before. This is actually in the interest of documented workers, as there is then less demand for undocumented workers.