Yes they do exist and they are popular. Flip flops are supposed to be quite minimalist footwear and not do a lot to the foot. There are however, many different brands of flip flops that are on the market for those who like this type of footwear and do need some sort of arch support. They are often used by those who need foot orthotics or supports which do need good footwear to fit them in, but they do not want to always wear that footwear. The arch supporting flip flops are a good alternative.
A popular brand in Australia is the Archies which are commonly sold in a lot of podiatry clinics. They were designed by a physiotherpist and come in about a dozen different colours. The amount of arch support in these Archies are similar to what you would be in an over-the-counter foot orthotic, so there is no reason to assume that the amount of support that they offer is similar. Some podiatrists have got innovative with them and added some unique modifications to make them more supportive.