A question regarding National Health Insurance

I'm very much a former (and possibly future) resident of Tokyo, but I'm trying to work out a potentially very embarrassing situation, and reckon the folks here might be able to give me some reassurance.

The long and short of it is that I was an exchange student in Tokyo back in 2015-2016. I lived for a few months in Taito-ku in a sharehouse, and later a few months in an apartment in Sumida-ku with my girlfriend.

I'm hoping that it's just a failure of my memory, but I can't recall paying for National Health Insurance.
I would have definitely been informed that it was mandatory (I have emails mentioning it). I know the post situation at the sharehouse was a mess, but I just can't recall receiving any bills in either place, or paying them at the ward office/at a konbini.

Basically, what I'm hoping to confirm is that if I hadn't paid in the necessary National Health Insurance contributions that definitely would have come up at either/both of the Ward Offices when I registered that I was moving out, right? It feels like that isn't something they would just ignore?

by throwaway_gos