[er35826]

And there's only one narrow failure mode where a dishwasher can actually fill up with water: If the drain is blocked. Any other failure mode (broken water heating element, broken agitator, power failure) still allows the water to drain so it won't flood.

[masklinn]

True, noted so in an other comment I believe but forgot it in this one.

As you hint it's a very rare mode of failure, and dishwashers don't use much water — a modern energy-star compliant dishwasher uses about 15L (~4gal) per cycle and the most efficient ones can go lower than 12L (~3.2gal) — so in most cases a blocked drain will end up with visible water staying at the bottom of the dishwasher and may not even overflow it to the door. The drain would need to be blocked directly at the top of the dishwasher drain, and seriously blocked (e.g. your asshole brother plugging it)

[prof_hobart]

Most maybe. But from personal experience, I can assure you it can happen. And it makes a fair amount of mess when it does.