Wild boar are a huge problem in Germany, as in America. Recently a hunter got killed by one. The article mentions that with the increased planting of corn (due to its high price), there's more fodder for wild boar, so they are undergoing a population explosion.
In America, a guy is on trial for being the "Johnny Appleseed" of feral hogs in Minnesota - although farmers there probably think of him as a biological terrorist. He's already blamed for the appearance of wild boar in tens of counties (with the associated crop destruction) and two pseudorabies outbreaks in domestic swine herds. Pseudorabies is absolutely awful for the owners of those herds; if the government finds out that you've got pseudorabies in your herd, they put them all down.
That brings up another interesting issue: a lot of people who keep rare breeds of pigs raise them outdoors, where they can catch diseases from wild hogs, badgers and other wild animals. In some cases, this has been disastrous. E.g. you've got a GOS producer who lost his herd due to bovine TB, which they caught from being outdoors. On a bigger scale, Spanish farmers have had to kill large numbers of Iberico due to diseases like Classical Swine Fever. Now that they raise them indoors more and more, that's less of a problem.
One argument says that if your goal is to preserve rare breeds, you should be wiling to do use technology to do it. E.g. raise them indoors away from wild animals, and use modern techniques like hormones and embryo transfer to increase their numbers - and even use techniques like cloning or gene modification. I don't think that most people who say they are in favor of breed preservation are aware of what breed preservation really entails.