Right about now, while doing a stocktake you will be going around the shop collecting damaged stock and unsellable stock.
Here is an idea.
Instead of discounting it to zero makes either a buy one gets one free group sell or a 3 for 2 special deal.
Alternatively, bundle the unsellable item with a sellable item in a group to sell it, e.g. an old magazine worth nothing can be packaged with a new popular magazine's edition. The proposed buyer will be rapt as they want one magazine, and they are getting the second free. You are rapt too as it a sale you may not have got, and it cost you nothing as the old magazine is worth nothing.
What you will notice is that your customers will tend to see this as an add-on reward so less likely to devalue your brand in the minds of the customer by excessive discounting.