My 2 cents. Vulnerability is a "side effect" of existing code. So if you consider the vulnerable code, it belongs to the owner of the rest of the program. If you write an article about it, you can cite the code and own the article. If you write an exploit, the exploit code is yours. And you can't patent the vulnerable code because it already is existing previous work.
Just like a poem can contain figures of speech like metaphors, you don't generically actually own "metaphors" but you can own an actual metaphor if it's written as part of your poem. Maybe the metaphor is too small and you cannot protect its rights, but if you are the legitimate creator, it's still your metaphor.