A tiefling can become undead

A typical tiefling that possesses the type outsider and the subtype native can become an undead just like any other living creature can, respecting, of course, the existing rules. To be clear, such a tiefling's appropriate death by a bodak, wight, wraith, or shadow wouldn't create spawn as such spawn can only come from a creature that possesses the type humanoid, and such a tiefling can only gain the vampire template (hence becoming an undead creature) from a vampire that's base creature type is outsider.

(To be honest, I gave up on trying to find in the list of hundreds of undead creatures a random undead monster that could transform a such a tiefling into an undead, which may lend some weight to a literalist argument like A tiefling killed by a typical Paizo-published undead won't create spawn. However, as this is Pathfinder, I'm certain an undead monster exists somewhere somehow that can kill a tiefling and see that tiefling become its spawn.)

Further, if a necromancer desires to animate such a tiefling's corpse via the spell animate dead et al. or see that corpse transformed into an undead creature via the spell create undead et al., that's totally legit. A tiefling corpse is just another corpse. Similarly, such a tiefling can, at the GM's discretion, become a lich.

The only counterargument that I can imagine that would disallow a tiefling from becoming an undead creature is the outsider type trait that says

Unlike most living creatures, an outsider does not have a dual nature—its soul and body form one unit. When an outsider is slain, no soul is set loose. Spells that restore souls to their bodies, such as raise dead, reincarnate, and resurrection, don’t work on an outsider. It takes a different magical effect, such as limited wish, wish, miracle, or true resurrection to restore it to life.

Keep in mind that when a creature gains the dead condition "[t]he character’s soul leaves his body." Together, what the core rules mean when an outsider lacks a dual nature is unclear vis-à-vis the status of the outsider's remains. (I am unaware of how this lack of a dual nature is handled in other Pathfinder sources.) For instance, a GM could rule this lack of a dual nature sees a normal dead outsider's soul simply snuffed out when its material form is slain therefore leaving remains suitable for, for example, animation as a skeleton, zombie, or whatever. (This reader believes this the path of least resistance.) Alternatively, for example, a GM could rule that a dead outsider's remains vanish, it's soul spiriting away its material remains to their (or its more properly) final reward; this would, obviously, leave insufficient remains to be animated.

None of this may matter to the tiefling that possesses the subtype native, though. That's because that outsider type trait continues, saying, "But this An outsider with the native subtype can be raised, reincarnated, or resurrected just as other living creatures can be." Although not stated outright, to this reader that implies that the whole lack of a dual nature thing at least largely—if not completely—doesn't apply to tieflings and other native outsiders.

Still, another, stricter reader or GM may disagree, saying the lack of a dual nature still applies to tieflings normally, the changes made by the native subtype applying only to those specific spells, and that, for example, the typical tiefling's remains—as explained above—vanish when it dies, preventing effects from occurring to its corpse after the tiefling's death, like spawning undead or whatever. This player would view that as a long road on which to travel, though, and a GM that rules in such a way should make that ruling clear to players that are considering PCs of any race that possesses the type outsider and the subtype native.