This spiritual 'fox' bestows a kitsune their trickster and warrior instincts and aptitude, as well as their supernatural abilities. A kitsune's fox spirit can be accessed, brought forward by a kitsune's ability to wield weapons, explained by Ken Yukimura or by their indulging in their elemental abilities. The fox is also affected by a kitsune's Tails in an adverse manner from what's been seen so far. In Thunder kitsune Kira's case, her swordswomanship or affinity for electricity works as a metaphysical gateway to the fox. Her shuriken Tail was once used to subdue the fox during a lethal loss of control.
Latent
When a kitsune is in their younger years, when their powers first manifest, the fox will awaken but will be dormant and is nearly inactive. The spirit is docile and Kira was in complete control of her actions, even when she began to actively learn to and use her abilities. In Season 3, Kira first became aware of her fox spirit when she took flash photos of herself seeing the entity around her. Her kitsune abilities completely awoke after her attack by mass murderer William Barrow. Barrow had attempted to kill Kira by electrocution, unaware it wouldn't even harm a Thunder kitsune and Kira's powers were triggered. Her fox spirit, her aura was later witnessed by Scott using his werewolf vision. He describes the entity around her like an armor around Kira's frame, that it's protecting her from harm.
Possession
In Season 5, Kira was forcibly experimented on by the Dread Doctors. They conducted a lightning bolt to empower Kira, augmenting her Thunder kitsune powers. Her fox spirit was wounded and empowered as a result. Later on, Kira's fox part began to jump out and during times of immense dire, fight-or-flight situations the fox would suddenly and sporadically take control of Kira, possessing her and have her commit actions that were totally out of character for her. Kira would also remember nothing from her blackouts.
Kira's fox was shown to be abrasive and bloodthirsty, and fluent in Japanese, even though Kira knew no Japanese at all. During the fight against the hapless chimera Lucas in 5x04 - Condition Terminal after he was non-lethally subdued, Kira was possessed by her fox then moved to behead Lucas with her sword though Scott stopped her. Later she attempted to kill her mother, Noshiko, during a sparing session, but Ken snapped Kira out of her possessed rage by using her shuriken Tail in 5x07 - Strange Frequencies, showing a kitsune's tails have an effect towards the fox. In 5x17 - A Credible Threat, Kira was possessed once more attacking Scott and Lori Talbot, but Scott pulled her back with his alpha's voice as Kira was an official member of his pack.
Kira's behavior was because of the balance of power had been swayed out of Kira's human hands towards the fox, explained by Noshiko. She also said if the power-hungry fox part of Kira became too powerful it would consume Kira' s humanity and life leaving only the fox. This probable condition implies this was the fate of the Nogitsune as he had no humanity and no original human body, only that of whomever he possessed.
Merged
A kitsune, with proper training, can learn to exert control over their fox spirit and tame them even after they have been previously overcome by the fox. The concerns and priorities of the kitsune become those of the fox's and a kitsune has total control over their actions.
This can be achieved through training with other animal spirits, similar to that of Kira's training with the skinwalkers. Mental health, balance and mental strength can serve to overcome the fox and help a kitsune know their limits. Noshiko attempted to help Kira regain control over her inner fox spirit through acupuncture. Ken also advises Kira that to tame the fox, she should use her mind as a weapon to "outfox the fox."
In 5x20 - Apotheosis, Kira, partially returning from her training from the skinwalkers, had tamed her fox spirit with complete control over her actions and abilities in time to help her friends against the assembled villains and dangers. She was able to use all her talents, her swordswomanship, strength and abilities safely.