Sure, they do. It all depends on how much the cat sheds and how much undercoat they have. I have a DSH that can be a worse shedder than my DLH - I have to keep him brushed regularly to prevent hairballs and to prevent fur all over things.

Higher quality foods can help reduce shedding. And keep up grooming her - various deshedding tools may help. A furminator or zoom groom, but neither can be used daily, though, because they will pull out too much fur and damage the coat.