Precisely the case with SVB as of this very moment - a sunken bank that does not have enough assets to cover its deposits is being bailed out by the state.
By the state and taxpayer money, make no mistake - even if the funds will not directly come from the US govt., the fees that they will impose on the banks by using the nation-wide bank insurance fund will eventually get imposed on everyone with a bank account in the US by those very banks in turn. So again, the public will pay.
Actually, its beyond using taxpayer money - if you are a taxpayer and your children have bank accounts too, they will also pay the fee instead of just you paying a tax.
(1) Shareholders aren't zeroed in a bailout
(2) The government pays for a bailout
Neither is true here.
If uninsured depositors took losses in the run on SVB, lots of other banks were going down too in the coming weeks. I think the argument is not that SVB is getting bailed out but investors in all the other poorly funded banks that won't fail.