Well, it all depends...some are saving money for such things through their Health Saving Accounts...if they are poor, they will be covered through programs already in place...there are lots of places that raise money for people in need without means...etc...hospitals provide financial assistance/discounts...
I am sure you know all these...:-)
btw, anyone who believes in the myth of utilizing less ER services with availability of Healthcare for everyone should take a look with what's going in MA (thanks to Romney(sc) )...their ERs are going broke (because their healthcare is "free", people are using ERs as primary services)...