According to an immigration lawyer I'm friends with, the better and more accurate term would be undocumented immigrants. Since, you know, their legal status isn't necessarily illegal/breaking the law, just that there is no paperwork for their presence.
What I find strange about this reasoning is that anyone who goes through the legal immigration process will absolutely have documentation. Even if they lose their own copy of the documents, several government agencies will have records of their own and there is a process to obtain replacements.
In other words, the odds of someone being in the US legally with no government issued paperwork or documentation to justify their presence is slim to none. It’s far more likely that someone lacks documentation because they didn’t follow the process set forth by the law to begin with.
The other side of this is that by calling undocumented non-citizens "illegal immigrants" you are calling the human "illegal" which is demeaning and also raises the question of how a human being would be illegal in the first place. Furthermore, if someone overstays their visa but entered legally, it's a civil but not criminal offense. So it's best to use language appropriately.
