There is constant speculation that Apple will introduce a cheaper basic version of the iPhone to address more of the market, and to fend of price competition from Samsung. As Apple seems to be doing just fine with the old phones, it would only make sense as a way to get rid of the old dock connector, and switch the entire lineup towards the lightning adapter.
How would Apple differentiate such a phone from the main phone? Until now it has used the available memory as the key differentiator, and it could do that with a cheaper version as well. The iPod touch also has a slower processor, as well as a slightly worse back camera than the iPhone. I doubt they would skimp too much on materials and the screen, as they are what sets the Apple brand apart. After all they have never chased the volume market in computers, and the health of the app ecosystem is excellent, so there is no need to chase volume to get more developers to their platform.
Currently Apple is able to charge more than 100% profit markup on the iPhone, and this gives them a lot of room to reduce prices for a basic model and still turn a decent profit. What I do not expect the basic model is to be cheap, more a different take on the iPhone, maybe the robust phone? Still elegant, but tougher, heavier ( like iPhone 4 heavy).
I do not believe that Apple will cut its margins on the phone too drastically, and definitely not at the price of quality. You use your phone simply too often to be willing to endure quality compromises, and in the developed world people earn enough to support a $100 surcharge every few years to get the quality you want.
Based on iPad mini as well as iPod Touch prices, a $350 iPhone is easily achievable, possibly even $300. The question is what kind of pricing pressure it would cause on the main model. Say it would be the current Touch with phone radios ( no LTE) added. Should they also provide a 32GB option for $400, I can see 60% switching from the 5 to this model. After all it would match or best the 4S in everything but the rear camera.