Same thing as if everyone stopped paying any type of loans. A shock to the banking system, potentially a collapse if the debt in question is a significant percentage of all debt. Many people would lose their savings.
And no don't hope that bank owners would absorb the debt, they would just liquidate the bank in a bankruptcy wiping out everyone's deposits.
Edit: In most countries there's also a deposit insurance scheme meant to cover cases of bank failure. But it can cover one or two banks failing, not all of them at once.