Sudden unforseen and expensive illness in the family isn't really all that common though. Furthermore, it is only really a problem in countries such as the US which don't have affordable healthcare for the poor.

There certainly are many people in this world that are poor because of a series of very unfortunate incidences that put them at a disadvantage. However, I think it's pretty clear that despite how common that may be, it cannot begin to explain the majority of poverty in "1st world" societies.