I think that the spider will catch food when it is hungry, and I am thinking that it is probably a very small spider so It probably doesnt eat much at all. Or maybe it has some dead flies somewhere in the web that are all wrapped up that you cant see?
If you are still worried here is some info I found on a website:

What do spiders eat?
Spiders eat invertebrates (insects and other small animals without backbones) and larger spiders may eat small vertebrates such as frogs and some birds. Spiders in Australia have all developed many different ways of finding and catching food. Some hunt for prey at night while others hunt during the day. Some prowl around and pounce on their prey while others wait for prey to come to them. Most spiders inject their prey with venom from their fangs. This venom helps dissolve the tissues of the preyís body so the spider can ësuckí it up as a liquid.

Hope that helps.