There are times when you might be forced to close a trade for more than its theoretical maximum. In other words, you might have to “offer arbitrage”and pay more than the maximum loss on the trade to close it out. This can happen when a defined-risk spread is and expiration is near. In order for the counterparty to cover their costs and at least “make something”, they will only take the other side of your closing transaction, if you are willing to overpay to close the trade.
Still, even though you will be paying more than maximum value to close that spread, it is most likely far less than the exercise fees you would be charged upon assignment.