Kai died 2008 years prior to the events of the Lexx premiere episode "I Worship His Shadow", defending his home planet Brunnis-2 against attack by His Divine Shadow's personal flagship. This valiant but desperate defense failed and His Divine Shadow destroyed the Brunnen-G home world. Knowing all was lost, Kai rammed his small fighter craft into the control pod of the Foreshadow in an attempt to destroy His Divine Shadow. Though he succeeded in ramming the pod, Kai did no significant damage, instead catapulting himself out of his cockpit and directly in front of His Shadow, who stabbed Kai and drained his memories.
Instead of having Kai's carcass incinerated, His Shadow had him "de-carbonized" and turned into a Divine Assassin, a nearly unstoppable killing machine in the direct service of His Shadow. As an undead assassin/ex-assassin, Kai's uniform is a blackened version of the colorful clothing the Brunnen-G had worn; his beehive hairdo, however, remains unchanged.
For the next 2000 years, Kai killed an untold number of heretics and revolutionaries in His Shadow's name. This changes when he is called to secure the Lexx from heretics. The Time Prophet had made a prophecy that the Brunnen-G would destroy the Divine Order and, with Kai being the last of the Brunnen-G, the responsibility fell on his shoulders. The current incarnation of His Divine Shadow refused to believe in the prophecy and called Kai to action as an assassin to mock the prophecy and show his own mastery of the Universe. Though Kai is nearly successful in his duty, he is called away by the Divine Predecessors, former incarnations of His Shadow whose brains have been preserved, who are under attack by a cluster lizard, a vicious animal which feasts on the flesh of the living and has a particular taste for brains. When Kai picks up a piece of the brain of the Divine Predecessor that killed him, he regains his memories and his free will. Over the series, Kai begins to remember small personality traits he held before he became an assassin, such as enjoying fishing and a "fondness for balloons".
At the end of the final season, Isambard Prince, former ruler of Planet Fire, restores Kai to life after promising it as a prize in a chess game. Prince visits the Lexx as a self-proclaimed omen of death, which Kai "feels" is meant for him. Kai says farewell to Xev and Stan before leaving Earth, apologizing to Xev for never being able to love her the way she wanted and they kiss.
Fulfilling his own prophecy, Prince restores Kai to life only minutes before Kai sacrifices himself to destroy the asteroid-ship harboring Lyekka and her kind. Kai is last seen flying through the interior of the asteroid with a particle collider, singing the Brunnen-G Fight Song, and finally crashing at the asteroid core with the device. Surviving the crash and finally alive, but next to the about-to-explode particle collider, the last shot is Kai laughing.
As a Divine Assassin, Kai is for all intents and purposes indestructible. Because Kai's body is "de-carbonized", it is heavier and significantly more rugged than that of a human. His body can withstand extreme heat and most forms of energy at extremely high outputs. He does not need to breathe, either. Kai can, however, be dismembered with relative ease. Despite this, being dismembered is usually not an impediment, as Kai can independently control every part of his body regardless of whether or not he's attached to it. This includes being split in half or beheaded. Furthermore, he can reconnect his severed body parts within moments simply by holding them together.
Kai's favored weapon is his brace, a clamp-like bladed device that emerges from his wrist. The brace can cut through virtually anything at Kai's discretion, and can alternatively clamp onto objects, either to drag them to Kai or allow him to drag himself to a desired location. The brace is attached to a line that can travel enormous distances (though never explicitly given a limit, it can at least reach dozens of stories), and can change direction mid-flight. The brace makes the sound of a screaming falcon when it is deployed. Even in the absence of this, Kai is far stronger than an ordinary human.
Because Kai is a Divine Assassin, however, he does occasionally fall prey to the programming embedded in his design despite having free will. If ordered to kill someone while in cryostasis, he is compelled to carry out the command; several students accidentally turn him into slasher movie-style killer by giving many confusing commands in this manner.
Kai is animated by protoblood, a substance secreted by the Gigashadow (the vast insect body of His Divine Shadow). This liquid can only reanimate Kai for a limited amount of time, so he must remain in cryogenic suspension between bouts of activity to prolong his existence.
In terms of ability, once Kai has been called to action, there is usually nothing that will keep him from killing whoever he has been asked to. As he explains at one point, he was once ordered to kill Ring Torbin, the rebel leader on Phoebe 27 who had buried himself deep inside the molten core of the planet, protected by fifty thousand men with robot controlled ion weapons. Kai killed 2,807 of his men before killing Ring Torbin. Kai can be delayed by various means, such as freezing or a simple lack of adequate transport (being ejected into space, for example), but Kai is resourceful and will often get around such delays.
A lesser limitation of Kai's undead state is his inability to perform most bodily functions. He doesn't need to sleep, eat, breathe, or expel waste materials (as he once tells Stanley, "the dead do not poo"). In one episode, however, he does use the toilet to remove an alien carrot embedded in his rectum, an experience he describes as "dry". He is incapable of (and uninterested in) having sex, a major disappointment for Zev/Xev, who lusts after the dead man, and the many other women (and, in the last two seasons, 790), who lust after him over the course of the series. He also claims to lack motivation and most emotions, and is unable to love, care, or truly feel for others. Despite his claims of emotionlessness, however, his dry humor frequently gives the appearance of expressing passive-aggressive disapproval of the other characters' actions and resentment of the fact that they often overlook the fact that he is dead. His actions can be rather ambiguous, as can his emotional claims (i.e. care for Zev/Xev near beginning and end of series and his feelings toward his dead race). The question is never directly addressed as to why he goes to such lengths to protect the Lexx crew, but he seems to possess a certain muted affection for them even when dead, and several times he's called Stan and Zev/Xev his friends. Also it is claimed he is emotionless, in the first series he shows considerable amounts of affection towards Xev. In the Giga Shadow for instance, when he loses his protoblood and falls, he says to Zev: "Farewell Zev, My..." then passes out before finishing. Also in the final episode of the series he apologizes to Xev for not loving her the way she wanted and they kiss, showing he may in fact love her, just not in the way she wanted. His flux between the amount of affection he showed her throughout the series was explained in an "In the making" one of the episodes in the third season. One of the creators stated that it was not because Kai did not supposedly feel but because he knew that life and death were not mutual and would ultimately leave Xev/Zev in sadness. Therefore resulting in his 'dead' reactions to her advances there on after. Once again becoming another display of his logic that would require some kind of feeling that he apparently 'lacks'.