I worked in retail grocery, but I would imagine the situation is the same in other retail outlets. Everybody who has replied so far has a piece of the answer. Sometimes the sale item is a “loss leader,” sold below cost to bring customers to the store, where they’ll buy other products at the same time. Sometimes the price is jacked up before putting it on sale to hide a price increase, or take advantage of the anchoring effect. Sometimes stores take a loss on a product that isn’t selling well, and they just want to get rid of it to free up space. And sometimes the store’s buyers got a really good deal on purchasing inventory, for many possible reasons, like a bulk purchase, supplier clearing the warehouse, or pre-booking the order well in advance. (Manufacturers often give discounts for guaranteed purchases.)

But, yes, as you suspect, sometimes the markup is outrageously high, and they can still make a profit when offering 50% off. (Not often in grocery, which is a low-margin business.)