How exactly does one break the bank?

If you got that much it's prolly best to stash it offshore 👍

The definition of the word break is muddled. Informality in usage brings like a change of circumstances or the emergence of a thing. Example: To break out the good stuff. Or, at the break of day. And so To break the bank simply means to avail one of access to funds [emergence] from within, which alters [breakdown of balance sheets] the balances within and expenditures from without.

The economics teachers would have instructed us but they aren't permitted to exceed the boundaries of their specialty by treading upon the field of linguistics specialties by challenging wrong teachings.


DISCLAIMER:
I may have just only pretended to know something about this. Feel free to disregard it if you find it offensive, insensitive or otherwise prejudicial to one of the liberal sensitivities and political correctness do thingys.

Lehman brothers?

Mostly either governments will nationalize them or use quantitive easing (ie printing/creating new money) so they do not go under.

Uk has used both methods since 2008

Savings and loan candles and the housing crunch.

By breaking into bank

It's an idiom.
It refers to a successful gambler has won more than than the house can pay out !