Q: how would you analyse the function of the VI in a I VI IV progression? (example: toby fox's "fallen down")
A: first i'd translate it to arabic numerals (or even just pick a key and use letters) because roman numerals make my eyes bleed (that's just a personal issue i have). then, checking what the song sounds like, i'd consider it more specifically than what you wrote. i'd say it's Dbmaj7, /, Bb7, /, Gbmaj7, Gbminmaj7, Db, Ab. (actually the whole thing seems to be tuned somewhere in between the key of Db and D, so don't take those chord letters as absolutes necessarily. still only using them for relative purposes)  as for your question, my analysis of the function of the Bb7 in this case is: it's musical. it reminds me of things i've heard in other music, and, this song is, in fact, music, so this doesn't surprise me. reading back over this it occurs to me that you might not think i'm serious, but i am in fact dead-on serious about all of this. music is precisely what's happening here, and that's no joke. i've dedicated my whole life to this stuff