They aren't, strictly speaking, undead (elementals were never alive to begin with), but these "predamentals" are to regular elementals as vampires, ghouls and the like are to ordinary humans: by feeding upon the life force of those they slay, they extend their ability to stay on the Material Plane. The exact metric is not known, but obviously, the more powerful the prey they consume, the longer they may stay upon Pellatarrum.
Excellent examples of the earth and water types can be found (warning: Cracked.com link) at The 5 Most Spectacular Landscapes on Earth (That Murder You).
Centralia, Pennsylvania is a great example of a fire predamental. On the one hand, it doesn't look especially active; on the other, it's basically killed an entire tow. It's also spreading, there's no way to put it out, and no one knows how long it will burn (it's already been burning for 50 years now.)
I don't have a good real-life example of an air predamental. Yet. Perhaps a reader can suggest a location where random, strong gusts of wind have caused people to fall to their deaths?