They are not "illegal immigrants" because people cannot be illegal.
On the other hand, "undocumented immigrants" makes it sound like the only problem is they forgot to fill out some paperwork, when the real problem is that if they had done so they would have been denied entry. (Not for any good reason, but that's another discussion.)
They are "impermissive immigrants" -- they are in the country without the required official permission. That is all.
In any case, they are immigrants -- it is completely dishonest to deny them that name, to limit it to those present legally.
On the other hand, "undocumented immigrants" makes it sound like the only problem is they forgot to fill out some paperwork, when the real problem is that if they had done so they would have been denied entry. (Not for any good reason, but that's another discussion.)
They are "impermissive immigrants" -- they are in the country without the required official permission. That is all.
In any case, they are immigrants -- it is completely dishonest to deny them that name, to limit it to those present legally.