As mentioned above it differs from country to country.
In Australia (and I'm sure this is the case in most countries) whilst you're meant to have a passport to arrive, Australian citizens who can be verified can fly without a passport back home (ie you've lost it or it's expired etc). It's highly frowned upon but there is a procedure to make it happen and whilst I've never tried it, I've heard reports of it being possible however often the biggest problem is the outbound country letting you out. Some countries don't really care as much whilst others like Indonesia or China are very strict on that sort of thing and want to see a passport upon you leaving.
Pre covid there were also flights that left the Australian east coast (SYD/MEL/BNE) and flew to New Zealand (AKL/CHC). These flights departed at 6pm local time and were often scheduled to arrive in New Zealand the same day but at 11:59pm. For travel between Australia and New Zealand your passport just has to be valid the day of travel (no 3-6 months validity stuff) and I've heard on numerous occasions of people traveling on the same day as expiry however more often than not the flight was 5-10 minutes late and by the time the traveler got to immigration it was the next day and the passport had therefore expired. In all cases, they let the passenger in with no problems.