Can Heroes continue to use their upgrades once they've run out of Hero days?
From what I have seen, Hero upgrades that require an action stop working, but passive upgrades stay active.
This means you cannot use
- Kitchen
- Home Laboratory
- Siesta Time™
But the following stay active
- Fence
- Large Curtain
- Lock
- Reinforcements
- More storage
And I believe that the Rudimentary Alarm will keep working, but I have never seen anyone with it.
I believe badp is correct, but it should also be mentioned that if you later add more hero days (while in the same town), you can then start using the things you had built earlier again. So they aren't exactly wasted, just dormant. I'm not sure about the defense bonuses though. I believe they still apply during the attack on your last hero day, but they may disappear after that.