To get more specific on the reason why Na and Cl ions decide to pair up and there are no free ions in an evaporated solution of a particular sample, say ocean water, you must bring the effects of water into account.
Technically, oceanic water contains other ions, i.e. Mg2+, Ca2+, but we'll ignore these for simplicity because some pretty strange things can happen with those ions and what you know of as the salt crystal.
In any particular sample of salt water, Na and Cl ions are insulated from each other by water molecules, such that their charges are stabilized—their charges are spread out over a larger area.
However, even with the added solvated effect of water, the Na and Cl ions still have a really weak ion-ion interaction. So when the solution is evaporated of all the water molecules, you're left with those Na and Cl ions completely paired, with no free ions. This weak interaction between the ions in solution (in water) lock them into place in such a way as to direct them towards each other again so they can reform the stronger, former ionic bond as water evaporates.