The bank will never lend money at a negative interest rate, but it could absolutely find itself in a position where the "market rate" for a loan is negative (i.e., the bank hypothetically has to pay someone to borrow money). In this case, the bank simply doesn't underwrite any loans. You can theoretically borrow money at a negative interest rate, but nobody is there to lend you the money.
Note that there's no special distinction between low and negative interest rates in this situation. You already see the effects of this when interest rates are low, even if they are still positive.