Can an elemental that's called be turned into an undead creature like a zombie?
I am unaware of the game saying specifically that a creature that possesses the subtype elemental is forbidden from being transformed by the spell animate dead into a zombie. However, I am also unaware of the game saying that a PC can't enter play with a dozen rings of three wishes and Cthulhu as a pet. Seriously, the game doesn't say a lot more than it does say, and it relies on readers to fill in the gaps. The short version? Ask the GM.
The long version: The restrictions that the spell animate dead has on transforming a corpse into a zombie are that a "zombie can be created only from a mostly intact corpse" —and there are remains when an elemental dies—and that the "corpse must be that of a creature with a physical anatomy"—but the game doesn't define the term physical anatomy, and that's kind of a sticking point. Even if a reader just hits the darn dictionary to define those words, whether the author of the animate dead spell intended readers to emphasize the word physical (as opposed to, for example, incorporeal), the word anatomy (as opposed to, for example, being comprised a single undifferentiated mass animated by a spirit), or both is a mystery.
To be clear, an "elemental is a being composed entirely from one of the four classical elements: air, earth, fire, or water" (Bestiary 311 and emphasis mine) and "[t]rue elementals are simple creatures, thriving spirits animating bodies of pure elemental matter" (Ultimate Magic 108 and emphasis mine), and this reader can't know how a GM applies that information to the animate dead spell. It might mean that an elemental has sufficient "physical anatomy" for the the animate dead spell to turn an elemental into a zombie or it might not. Only the GM knows for sure.
By the way, there are, of course, a vast number of ways that a creature can be transformed into an undead creature other than with the spell animate dead, and an elemental just by virtue of of its subtype or its outsider type doesn't possess any particular defense against this grisly fate. If an elemental meets the criteria for transformation into an undead creature, it'll be transformed into an undead creature just like any other creature would. (For example, a vampire that was itself originally an elemental can use its energy drain ability so that its create spawn ability transforms elementals it kills into vampire elementals. And, y'know, I don't say it often, but good on Paizo for making that a crazy and weird possibility.)
Finally, the type construct grants immunity to necromancy effects, and as the spell animate dead is a spell of the necromancy school, a construct can't typically be the subject of it. In addition, the construct type grants immunity to a host of other potential ways that undead creatures use to transform other creatures into undead creatures. Nonetheless, given Pathfinder's vastness, I'm certain that there's an undead creature or some combination of spells or magic items or something that can get around the construct type's formidable defenses and, for example, transform an iron golem into some kind of undead iron golem.