Hi,
I came across this point なくなる while learning ようになる and I’m not sure if I’m being completely oblivious but I can’t find it anywhere on Bunpro/not sure if it’s actually related to ようになる and just not mentioned?
When you say なくなる, I think of the two verbs that pop up in this Jisho link: https://jisho.org/search/なくなる.
So, I don’t think it’s a grammar point, and it might just be a verb, depending on the context.
なくなる is just the appropriate grammar to express that something “becomes” ない, or else “ceases to be ある.”
Theoretically speaking, I think this grammar should be applicable to all い-adjectives and all intransitive verbs that express a state of being, but realistically speaking, I think there are probably some verbs that fit this criteria that would sound おかしい nonetheless.
Anyway, ~く and ~に are both adverbial suffixes (which means they modify the upcoming verb), and serve the same purpose for different parts of speech. Verbs/い-adjectives replace い with く, meanwhile nouns/な-adjectives simply append に. If you haven’t noticed already, I’d like to point out that the line between verbs and い-adjectives is very thin, and so they often behave/function extremely similarly. Likewise, nouns and な-adjectives behave extremely similarly. It may help to think of い-adjectives as a special type of verb, and な-adjectives as a special type of noun.
Back to your original question though. I personally don’t see any connection between なくなる and ようになる at all, apart from the fact that they both use なる.