All my villagers have died except my golden child. Is it possible to increase the population with just him? He will never die because he keeps producing food and all the puzzles are beat. It's been 3 weeks without any events, I don't check it everyday, but I thought maybe I would have an event that would bring babies in a barrel or something. Will I have any events at this point?

That has happened to several people before, and nobody has reported seeing any Island Events in that situation.

I have had only the GC left on one of my games for many weeks, and nothing has happened. No island events of any kind. He will never die, and I don't have the heart to delete his game and kill him...