In most areas it is unlikely that feral pigs can be exterminated. It is theoretically possible, but the cost to totally eliminate feral hogs in usually prohibitive. In addition, even though it is theoretically possible to control wild hogs, I still don’t think it is possible because of the areas they inhabit. With this in mind, landowners must generally accept the fact that they will always have some wild pigs, and should therefore plan for a long-term control program.
Feral hog damage can be extensive and costly if not controlled. Control for disease suppression is extremely expensive because many hogs would need to be eliminated, the density greatly reduced to slow (much less stop) the transfer of disease between hog populations.
Crop depredations may cease after one or two hogs are shot or trapped, or intermittent hunting pressure is put on them. They simply move to new areas. If hog depredations are heavy enough to require a reduction in the overall population, then a program can be very costly, depending on the size of the area involved. Keep in mind that wild hogs cannot be eliminated by shooting or trapping, both together or alone, but these actions can help keep hogs numbers under control — or on your neighbors property!