In a nutshell there is no such thing as 'unlimited' resources, whether it be bandwidth, diskspace or whatever. Someone, somewhere is paying for the resources that you are getting for free or very little - for the moment. Ultimately you will find the truth is that you will pay for it. See this article.
Paying for it, does not necessarily mean in cash money, you might find that your website goes down frequently, is slow etc.
Low cost hosting is just that, savings have been made elsewhere, possibly in the level of support and expertise you will get and most certainly in the most critical elements of all; the hardware and infrastructure.
When you are offered 'unlimited' resources, check the small print, we would put money on the fact that it's not really unlimited and there will be limitations imposed.
Many companies offering this are 'overselling', i.e. selling more server space than they actually have and then keeping thier fingers crossed that the customers wont actually use it. If they did it would be catastrophic! Those who do start to eat into resources are either punted off the system completely or told to move to a dedicated server, which will cost significantly more.

We do not and will not offer unlimited anything! You will know exactly what you are getting for your money before you buy.
No one actually needs unlimited space, bandwidth or anything else anyway - it's a complete nonesense and a ploy to trap the unwary.
Websites run on relatively little resources, less that most people believe. With the exception of those unsavoury ones - which we wouldn't host anyway :-)