I realize you just stated a case without offering an opinion one way or the other on it, so don't take what comes next as my having misunderstood you.
If a person is completely functional and comfortable and has no particular academic interest in language learning, then what does it matter if they stop? I'm very much like your friend's mother, other than the heavy accent bit. I haven't actively studied Japanese since probably sometime in the late 1980s. While others assess their level as "beginning", "intermediate", or "advanced" the only assessment I make of my own Japanese is "adequate to my needs".
While I think immigrants are under a sort of obligation (or at least ought to feel themselves to be so) to learn the language of their new environment I don't see that there is any obligation to go beyond the necessary and aim for the perfect. So long as they functional (and functionally literate) adults able to understand what is going on around them and figuratively speaking wipe their own linguistic rear ends, then they're not burdening anyone and society has no right to demand or expect perfection....especially when "perfect" linguistic skills are so often lacking among native speakers as well.