[reitzensteinm]

You're probably right you don't have to worry too much about the bank going bankrupt.

But if the primary purpose of the emergency fund is to smooth things out if you lose your job, that's literally the moment the bank will get cold feet about lending you money it's not contractually obligated to.

If the economic trouble causing your job loss coincides with a drop in house prices and all of a sudden you're underwater, it's hard to imagine a clause like that not being triggered, should it exist.