That's not true. As of December 31, 2022, Silicon Valley Bank had approximately $209.0 billion in total assets and about $175.4 billion in total deposits. Even if liquidating assets forced a 15% haircut, depositors will be made whole.
If a bail out is necessary, it's likely in the form of a short-term loan to make depositors whole sooner rather than later. And, such a bail out can/should be structured as a loan with significant interest in which case it's not really a cost to taxpayers.