The concept of price discrimination involves selling at higher prices to those who are willing to pay more and selling at lower prices to those who are not willing to pay more. A very slow going out of business sale can accomplish this.
When the store first starts "going out of business," it reduces its prices to a degree. People who are willing to pay that price come and buy. But there may still be people who are not willing to pay that price but who would buy the merchandise for less. Later, the store lowers its prices further. At this point, the people who are more parsimonious come and buy.
In this way, the store has essentially engaged in price discrimination. It has charged one price to the people who were more eager and more willing to pay a higher price. It has charged another, lower, price to those who were not willing to buy at the higher price. Thus, the slow going out of business sale, with progressively lower prices, essentially acts as price discrimination, thus increasing the profit the store can make.
It should be noted that many stores that hold going-out-of business sales are not necessarily just disposing of existing stock, although they may try to give the impression that this is the same as a "clearance sale." A store may be going out of business for six months or a year, bringing in truckloads of new merchandise in the back door as customers carry the other merchandise out the front. It isn't over until it's over. Often the only way to be sure the store is really finally going out of business is when they put the furniture and display racks and cash registers up for sale.