Imagine someone who learnt foreign language (FL) from the same language family as his native language (L1) for three years at secondary school and then continued studying this language at university. Let us assume that this foreign language is German (so this person's native language is another Germanic language). Then they neglect their German for 10-15 years except for occasional reading in the language. Then they move to Germany. They still have CEFR level C1 (close to C2), thanks in part to the similarity with L1.
After living in Germany for 7-8 months, they find that most German language courses for CEFR level C1 are not challenging enough and that C2 courses (if they are offered at all) have many participants who are at level B2, which decreases the effective level of these courses. So German language courses for non-native speakers look like a dead end.
They still notice grammatical errors in their own German, and that they avoid certain structures (i.e. pick alternative formulations on the fly) for fear of making mistakes. Otherwise, their speech is fluent. Native speakers (including colleagues) do not correct them. (Error correction appears to be rare among adults.) How can this very advanced learner get rid of the remaining grammatical errors in his German?
(I used German as an example, but it would work for any language, though the focus here is on languages from the same family.)