The reason a $100 par bond paying 2% sells for (I don't know, say) $87 when interest rates are (I don't know, say) 5% isn't that the original bond is impaired. It's that the same $100 buys you a bond that pays 3% better, so nobody will buy the bond without a discount.
But the bank doesn't normally sell the bond to begin with. That's why people say banks "borrow short and lend long". What the bank is supposed to do is hold the bond until it matures and is paid back in full. The only reason SVB can't do that is that all its depositors simultaneously demanded their money bank, so it couldn't wait the bonds out. But other institutions can do that waiting.