As the sibling noted, the order of borrowing and deposits does not matter. The summation will always be zero.

This gets to the heart of why there can be negative dynamics in a credit cycle. If I’ve lent 1 real dollar 100 or 1000x then there is a real risk of everyone needs that dollar back today. Similarly if creditors become risk averse and stop redepositing the money into the banking system, the velocity of money will tank and the number of dollars available to lend/spend will collapse. Growing the money supply only through fractional reserve dynamics also poses risks if a systemic imbalance emerges between creditors and debtors requiring some individuals/corps to be permanent borrowers e.x the Great Depression, and Recession.

In many ways the US is using treasuries to counterbalance the above by having the federal reserve purchase treasuries which will never be paid back in real dollars. However until the pandemic the government had limited ability to place those trillions of dollars in the hands of people who needed the surplus.

The sum of all credits and debits is zero (by the double-entry accounting definition), so seems like this is tautologically true, though not very useful.

The economic principle at work is you can have $1 in the bank and loan that to 7 people sequentially (who each redeposit it), or have $7 and loan it to those same people simultaneously (who each redeposit it), but in both cases the same transactions happened ($7 out and $7 in).