And yes, villagers can get sick while the game is closed. As Barbara said, it's good to have a couple of trained healers to to cure the sick if it is going to be closed without pausing. You need two, because like one of the hints say "Who heals your healer?"

I'm also sorry that you lost your tribe like that. I've lost a few early in the games, and my "no fshing" village was down to just a couple of kids several times, but with the GC's help I built up the food supply. You do get attached to them. My only problem now is when I want to start a new game, which village should I get rid of?!