If you are implying that BoA is in trouble if there is a bank run then yes, that applies to every bank in existence regardless of the circumstances. Considering their size, AUM and customer diversification (none of which worked in SVB's favor), there is a very low risk of that happening in this case.
BoA is a GSIB, meaning it’s deposits are essentially explicitly guaranteed as it’s not allowed to fail due to its systemic importance to a functional financial system.
That’s a small but dangerous jump. Deposits will be protected as much as possible but that doesn’t mean in a worst case event there can’t be a bail-in. Happened to Cypriot banks.
Just because it’s a GSIB doesn’t guarantee that the US tax payer would pick up the tab on all deposits if push came to shove.
I believe FDIC guarantees private deposits up to $250k. And FDIC itself is guaranteed by the US government so it's basically backed by a dollar printing machine.
Excluding deposits over 250k and non-personal deposits but I believe these are a minority for a bank like BoA, which is mostly retail.
GSIB is just a list made after analyzing the global markets in the wake of the 2008 crisis and those on the list have some additional reporting requirements, nothing more nothing less.
Also, SVB filed to raise equity capital thereby saying to the market they needed to raise money and we’re trying to do so. They could have been selling some of those liquid bonds at a discount and taking gaap losses.
In practice this might be true, but I'm not sure every bank would have a multibillion dollar hole in its balance sheet if all customers withdrew their deposits.
There's probably a point to be made that banks with large unrealized losses would lead to customers losing deposits, while banks with a positive net asset would not.
Most BoA deposits are likely guaranteed since they come from private persons and are below the limit. So a run is far less likely even if they are / get in trouble.