Is it illegal to have an expired passport?

This is a purely technical question. If you have a valid residence status (that is, your residence card is not expired), but your passport is expired, are you in breach of any (Japanese) law?

Just trying to settle a point in a discussion. Every other topic I have found simply tells you what to do in this situation (i.e. renew your passport asap), but I'm curious if you still need a valid passport to be residing in Japan legally.

Depends on the class of visa. if you have a permanent residence then many people have expired passports. For temporary visitors with temporary status there is a requirement to have a valid passport for duration of stay. Your question (interesting) as it sits in the middle.

When I did my visa it was never mentioned that I needed to retain a current passport, although it was submitted as part of the application (and I've just renewed it too). When I renewed the old one was immediately cancelled so I am without a passport until the new one arrives - I just can't travel/leave the country.

It depends on the situation.
If you have permanent residence, then passport being expired is not an issue. However, it can be an issue if you are about to renew your permanent residence.
If someone has a visa for a short time including one year visa,not having passport renewed should be a problem. Why, there is always a risk that your visa renewal maybe denied. So, you need a valid passport to leave Japan.
Passport is not really a huge problem but they may not like it when they see your passport was expired. They may take it as a negative thing in your visa renewal profile.
Just an opinion.

Right, I know you'd need your passport to leave/return (i.e. pass through ports), and I realize that having an expired one doesn't seem to be an issue otherwise practically, but from a purely legal standpoint are you supposed to have a valid passport to be in Japan?

I understand it's rather a technical question than a practical one, but I'm curious all the same.

No, it is not. For mid to long-term residents (immigration parlance for "people with a resident card"), the only time when a valid passport is required is when you enter.

In particular, even in cases when you normally present your passport, such as when extending your period of stay, a passport is actually not required: if you can't submit it, you can instead submit "a document with a statement of the reason therefor."

As an extreme example, a child born in Japan to two foreign parents (and thus not a Japanese citizen) could conceivably live his or her whole life in Japan without ever obtaining a passport.