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.

No, sudden unforeseen and expensive illnesses aren't that common. Sudden costs are. Costs don't even need to be unforseen, they just have to be more than you can deal with on a timescale.