When drug dealers, prostitutes, pornographers, and foreign tourists buy something today, they pay taxes (corporate, employee withholding, FICA, etc.) that are contained and hidden in the purchase price. The Fair Tax pulls them out and makes them visible.
What an illegal, for example, doesn't pay today is income tax. BUT, if we could somehow force him to pay that, he'd simply raise the price he charges for his service, meaning those who use his service (ie., us) would end up paying his tax for him.
Under the Fair Tax, the situation is similar. Let's see a show of hands of everyone who thinks the drug dealer will add the Fair Tax to the price of cocaine and pass that money on to the IRS. Ergo, there will still be cheaters.