Cosmetics brand Hard Candy is going through a change in identity.

While deep discounts on the brand’s Web site, which touted “75 percent off everything” last week, led to a flurry of speculation that the business was being shuttered, executives at the brand and its parent, Falic Group, refuted the rumor.

The company said that, for the time being, the brand will continue as a fragrance business as its core color assortment is phased out and new strategies are explored.

“We’re repositioning some parts of the brand,” said Jerome Falic, chief executive officer of Falic Fashion Group, who indicated that sales had softened on the...