My answers are: Yes, and Maybe.
Let us look at how retailing works. The retailer buys either from a manufacturer or a distributor. There will be standard discounts which will vary according to the trade and type of product. Basically it will also depend on how quickly the items are expected to sell and the risk if they remain unsold. For example, a newspaper or milk may be sold to the retailer on "sale-or-return" so effectively the retailer only pays for what they have sold, while the distributor takes back the day-old newspapers or the week-old milk. The retailer is expected to pay quickly but will always get a credit for the returns, often before the account has to be paid. That can mean they do not have any capital tied up but the percentage profit they make, whether calculated on the price paid by them (the cost price) or the price paid by the customer (retail price) is small.
On the other extreme, in the fashion industry, as it was traditionally, the stock changes either twice or four times a year, and has to be ordered well in advance of the changing season. When prices were stable the clothing store would bundle up the winter clothes as summer approached and store them until next winter. But fashions change and changes were encouraged by the trade, so the fashion end of the retail market would expect to sell the new season's clothes at a big mark up, at least double the price they paid to the distributor.
They would know that not everything would sell quickly but they needed stock in their store through the season. Their takings would become less as the season progressed and it was normal to offer discounts and, at the end of the season to sell whatever was left in a clearance, often at half price or less. That would mean they made no profit on the last items sold, maybe even made a small loss. But overall there would be a normal profit, provided they made the right decisions when they made the initial order. As an example, let's say they bought 100 dresses at $10 each. That's $1000 paid out. If the first 50 sell at $20, that's their cost back, and the remaining sales, let's say they all only sold in the clearance, at $10 (which is "at cost" or a genuine 50% off what they had been selling for, then overall they have made a gross profit of $500 on that original $1000. Out of that they have to pay all the expenses of running the shop.
The retailer buys most stock knowing that they are going to have to discount in the end so they buy on the basis that they must make a certain average margin across sales of the entire stock. Then they make guesses, based on experience, about how much of the stock they will be able to sell at "full price" and how much at various discounts. They then set up their "full price" (which might be +100% or even more of the wholesale purchase price) and their various discounts to give them -- on average -- the margin or gross profit they must make on selling the entire stock.
Now it starts to get complicated, because we have to cope with the opposing forces of increasing production costs, a rising currency conversion rate, changes in fashion and whether there will be a new, improved version of the product coming soon. With rising inflation and/or a falling dollar it will not cost $1000 to replace what cost they bought previously. It may cost $1050 or $1100, and those extra dollars have to come out of the profit from the previous season.
If changes are the other way, and the replacement equivalent will cost $900 or $950 then it may seem that retailer is doing better and has more than his $500 overall profit. We tend to have a well informed public and if it is an electronic product instead which is being cleared at "50% off" then even that apparently huge discount may not be enough, and so discounts rise even higher. The superceded TV or tablet may have to be almost given away once an announcement of the new version has been made. Much better to have sold it for whatever the retailer could get a few weeks earlier.
Things get even more complicated when a distributor offers increased discounts according to the quantity purchased. The savvy retailer needs to make a lot of calculations and include some informed guesswork to decide whether the extra discount is worth the added risk. If the extra discount is sufficient, then the retailer has to decide whether the incentive to the customer should be offered when he buys or after he has sold his expected number of items at what is now an additional profit. This decision may also be affected by whether the product has a use-by date.
Manufacturers make mistakes, especially with variations such as flavours or colours. They may make arrangements to advertise a "special" and give the retailer an incentive to have greater stocks at that time. The retailer with cash reserves may buy then knowing that he'll sell more "on special" and have sufficient left bought at the better price to cover normal sales for a period thereafter. This will not work if the manufacturer has packed the "special" with different wording, such as a date-limited competition.
My real estate friend was fond of saying "there's a price for everything". The skill was finding that price. To the savvy customer who does not mind having last season's electronic gear or fashion, and the product with an expired competition date may be at an attractive price in a clearance store.
If we are to continue to have suppliers in the future, whether on-line or physical stores, then it is not the profit on any individual item which matters, it is whether the retailer is making sufficient overall to pay for the replacement stock plus all the other costs, including a wage for the retailer, and thus progress into the next trading cycle.
This brief summary does not cover all the reasons why you can legitimately find products at "50% off", but I have a couple of further warnings: Beware statements such as "up to 50% off" where many items may be at full price or at a much lesser discount, and beware the second or third tier chain trick of have legitimate branded products packaged without a normal accessory or tool and compared with the price of the full item "elsewhere".
You should also consider reasons for purchasing other than price. Will the place you are buying from help if you have problems? Or just be willing to show you how a device works, or set it up as well as delivering it? Price isn't everything.
Gordon Woolf is a co-author of Success in Store: How to start or buy a retail business, enjoy running it and make money, available from Amazon and The Worsley Press.