Premise[]
It's a pretty common belief that Faora and the rest of the Sword of Rao survived being sucked into the Phantom Zone during the climax of Man of Steel. Just to be clear, I'm aware Zack Snyder said it was open to interpretation, stating he didn't know if Faora was alive in there. I'm going to set out to prove she's not.
Reasoning[]
Emil Hamilton confirmed the phantom drive technology in play would create a singularity if they succeeded in crashing Kal's ship into Black Zero. A singularity is a theoretical point of infinite density, proposed to be what black holes are. If Hamilton is accurate in his assessment, anything sucked into the singularity would be crushed into infinite density as well, destroying all form no matter how strong it was. There's room for argument, however, as Hamilton may very well be wrong or otherwise speaking colloquially about something that acts like a singularity without being a literal singularity.
Even if the "singularity" isn't a true singularity, it's the result of untethered technology that's otherwise used with major safety precautions. When the Black Zero is initially sent into the Phantom Zone, hauling the members of the Sword of Rao as prisoners, there's a projector set up to receive them. It stretches open a portal big enough to contain the ship, with a set of some sort of probes running the length of the ship, seeming to help it cleanly enter the Phantom Zone in some capacity. The technology is also used for quick travels in a seemingly simpler way, which is perhaps because using the Phantom Zone to travel through space is easier to do than traveling directly into the Phantom Zone, but that's unknown. Either way, those safety precautions used to bring the ship into the Phantom Zone are not present here, nor is even the protection of the ship's hull. Faora was protected only by her battle armor, while most of the others merely had on their skin suits. While the yellow sun has increased their durability, it's safe to say the damage they're receiving is greater than the force used to snap Zod's neck applied throughout their bodies, based on the effects of the warped gravity.
There is the possibility that the Sword of Rao members were warped to a new location in space, as opposed to being sucked into the Phantom Zone as stated in the movie. How would Clark or Hamilton know? In this case the warp point must either be one of the previous warp points of the two drives or a random point in space. Assuming the technology is still functional enough to recall a past warp point, the list of points is limited to Krypton, which is now dead, the Kryptonian outposts, which have already been picked clean, or Earth, in which case the Sword of Rao has been living in peace among humans for several years. The most likely of these would be the most recent warp point, which would be one of the dead outposts. Black Zero was sucked in with them, however it was at the very least severely damaged, if not entirely demolished. Faora and her comrades would suffocate on the planet's surface, or if they were lucky, it would have breathable atmosphere and they could attempt to repair their ship. Success doesn't seem likely, but if anyone wanted to bring back Faora and the Sword of Rao, this is the cleanest way to do it. It's a plausible scenario given what we know of phantom drive technology that also explains their extended absence.
Conclusion[]
If you take the movie at its word, Faora and the Sword of Rao are definitely dead. However, there are openings to bring them back, even without a level of cartooniness not yet seen in the DCEU.
