You can't clear your void, it's a myth.
I don't think it's a myth so much as it's got a "chance"
There have been a few times where I've tried to get voided villagers and have not. There have also been times where I've had 9 villagers and had many visitors and gone to many towns without ever picking up a voided villager~
My theory on the matter is that whenever you visit a town, or someone visits you, the game has a "chance" to dump a villager. If the RNG deems it so, the void reacts. If not, everyone stays put.
So if you visit a 10 villager town and the RNG tells your void to dump, it can't dump into that town because of the max. Therefore it "clears" because since it tried to dump and could not, it will not longer attempt.
The term "clearing your void" is a bit misleading since you are right, you can't CLEAR it. That'd basically mean skipping your 16 villager cycle~ But what these people are referring to, which is basically clearing the CHANCE for your void to dump a villager, does have some testing to back it~ The reason it fails at times is because, as I said, it seems to be a chance. So if you go to "clear your void" and the RNG doesn't land on a drop chance, you've essentially failed to do so.
It's just a theory but given my general experience with the matter and my slight knowledge of behavior from both this game and others, I think it has a bit of plausibility~ Take it or leave it though. That's just kinda how I think of it and I'm sure I'm prolly wrong x3