People would have at least a stock of water bottles, and I've heard as a recommendation if a typhoon is coming to fill your bath as well to use as gray water (flushing, washing yourself). I believe that's also why most families also have a small gas stove (with gas canisters), the common usage is usually to have a small party dinner with the stove for cooking in the dinner table, but it's also very useful in case of blackouts and you can probably survive eating cooked rice+whatever you find for few weeks if needed. I don't know if people store other foods (cans, etc) for emergencies, I should probably inform myself a bit better.
While Japan hasn't been close at all of a major blackout disaster like this for a long time (AFAIK), I cannot imagine how quickly e.g. Tokyo could get into chaos if there's a major prolonged food, electricity or water disruption.