https://en.wikipedia.org/wiki/Illegal_immigration#Terminolog... "undocumented" is a euphemism since "illegal immigrant" sounds like the person is illegal (vs having done an illegal action), but it has the unfortunate effect of leading to exactly this kind of confusion.

So-called "undocumented immigrants" can be quite well documented and even pay social security taxes: https://www.marketplace.org/2019/01/28/undocumented-immigran...