Remember when potbellied pigs came on the scene as cool new exotic pets? I do. It was around the mid-eighties. I recall wondering which I'd rather have, a miniature pig or a miniature horse. (The answer: Neither, though they are both swell. I'd rather have a miniature cat.)
The first breed was originally brought over from Vietnam for zoos by a man named Keith Connell, and were bigger than the usual pet pig size you see today. Two other breed lines were established here in North America, and the result is the handy variety of low-slung porkers available today. There are actually a number of varieties in Vietnam itself, such as the "Heo Moi." You can get the short but sweet info on that in this article.
Alas, people grow tired of their pigs, or suffer misfortunes, or coldheartedly traffic in them, and the pigs take the brunt of it. They are abandoned or poorly cared for, like so many "inconvenient" pets these days (an intense peeve of mine, since I've spent my whole adult life choosing housing that would take my pets). Luckily, there are kind souls out there for everyone, including a low-slung oinker down on its luck.
Just such a place is Ironwood Pig Sanctuary of Tuczon, Arizona. They have a good site full of pictures and stories, if you'd enjoy learning about the hearts & souls of a few pigs - and I think you would.