"Undocumented immigrant" does technically describe a person's status but it's only used in relation to certain types of foreign visitor. Across the white English speaking world we'll almost universally use "undocumented immigrant" to refer to brown-skinned people, while we use "visa overstayers" to refer to white-skinned people.
Some guy from India comes to work for a cousin's business on a sponsored work visa and stays a week too long? Undocumented immigrant.
Some white woman from the UK comes to work for a major tech company and stays a few years too long? She just overstayed her visa.
Then to round of the discussions about words changing in meaning over time, remember when holding thumb and forefinger together in a circle was just "the game" and you'd do things to get your friends to look — at which point they'd lose "the game"? But these days, it's only a white power symbol, thanks to some anonymous idiot on 4chan.
It's a crazy world that changes so quickly. I can understand why some people want the world to stay just the same for a decade or two. But that can't be done. We have to adapt or die.