Fake sunglasses don't have UV protection, but they can protect our eyes safe from harsh sunshine on a certain degree as well.
People buy fake sunglasses for fashionable appearance as you said. So UV protection isn't on their mind. However, if you can afford the real qualified sunglasses, that would be better for your own sake.
There is a difference between fake sunglasses and the replica sunglasses. Fake sunglasses only focus on similarities not quality. But replica sunglasses focus on quality and similarity. Usually, fake sunglasses often state that they present total UV protection,obviously they want to make a big sale. Actually, they lack much UV protection. You have to do the work of researching each product you are pursuing, and there is a useful website which will help you to know whether the fake sunglasses have UN protection.