Think about it like this: the sanity and the stamina numbers printed on each investigator card are the maximums for that particular investigator. If some game effect were to reduce that number to zero, there would be no way to recover from that. So, for instance if your investigator's maximum sanity was somehow reduced to 0, even if you went to Arkham Asylum, you couldn't receive any sanity because you can't receive sanity above your maximum, which is 0.
This is different from having your sanity to zero, because that doesn't impact your maximum sanity. You can reload at the Asylum (or pick up a madness) and get right back into the game.
Hopefully this helps. It always sounds really clear and coherent in my head.