Back before all of the banks were wired together, I had a friend with what we called a "bottomless ATM card."
He could withdraw whatever amount he wanted from the ATMs at college, but since that region's ATM network wasn't hooked up to his home bank's ATM network, it took months for everything to reconcile.
He could keep withdrawing, even if he had taken out far more cash than he had in his home bank account.
On breaks, he would go back home and pick up enough hours at his part-time job to cover the difference (it wasn't unusual for people to be paid weekly or in cash back then), make a deposit, and everything was fine. He just had to keep one step ahead of the computer batch processes.
Also, I think Chemical is Citibank now. I had a Chemical account, and a Dime account. I still think of Citi as "Chemical," though.