I think the additional liability from that event would be much less because it would be computed from the interest payments that the bank eventually owes the depositors.
So given an interest per annum of 1% (for example), a $1m deposit would add $1m liquid, non-earning assets while also adding $1.01m to their liabilities. So, effectively, they’d have $10,000 in unsecured liabilities.
To counter that imbalance (as well as protect the cash from the effects of inflation), they’d have to put some of that cash to work via various investments.
So given an interest per annum of 1% (for example), a $1m deposit would add $1m liquid, non-earning assets while also adding $1.01m to their liabilities. So, effectively, they’d have $10,000 in unsecured liabilities.
To counter that imbalance (as well as protect the cash from the effects of inflation), they’d have to put some of that cash to work via various investments.