If you are writing off uncollectible accounts receivable as they occur (the direct charge-off method), then there will be times when a customer unexpectedly pays an invoice after you have written it off. In such a case the correct treatment is to reverse the write-off, which will yield a negative bad debt expense if the original write-off occurs in a month earlier than the reversal.
On the other hand, if you are using the allowance method and charging an estimated amount to bad debt expense each month, an unexpected customer payment may not result in a reversal of the original bad debt expense. Instead, since the assumption behind the allowance method is that some receivable will not be collectible (we just don't know which one), you would normally not reduce the balance in the allowance for doubtful accounts.
Thus, the method you are using to record bad debts will be the key determining factor in whether or not you will ever experience a negative bad debt expense.