In the case of SVB, the bank is closed and has no assets: stockholders and bondholders alike are out of luck. But accountholders don't lose any money.

In theory, no bank ever owns depositor money. The money is accounted for separately from assets they own. That's why bank size is often measured as "assets under management." They are allowed to use it (customer money), but not to own it.

They are always required to hold customers' money plus reserves; their license to leverage and play with customer money depends on their ability to manage their reserves. With no reserves, they can't be a bank anymore.