He seemed to have the upper hand but was overconfident and left his guard down and Nail won with a surprise attack. Recoome is now healing in Freeza's spaceship after his defeat.
Recoome has a habit of underestimating his opponents, playing around with them and acting like pain is nothing to him. He is very loyal to the Ginyu Force, and respected his Captain Ginyu greatly. But to anyone who is not a Frost Demon or part of his team, he is generally disrespectful.
While he is arrogant to everyone who's weaker, he seems to have left an impression on Nappa, who on seeing Recoome after 40 years not seeing Recoome humiliated him, Recoome has the same flashback during his fight with Nail, cursing the fact that Nappa won so easily against a Namek, while he was having trouble. Unable to accept that Nappa greatly surpassed him, he tries to get up, but fails and gets knocked unconscious. He used to mock Vegeta, but Vegeta did not seem to bother wasting time on Recoome.
He also bullied Kiwi into taking a losing bet because he could, making Kiwi unable to enter the tournament. The bet was one they both knew Kiwi would lose, making Recoome seem to have a habit of bullying elite warriors, by constantly addressing the fact that he's at least twice as strong as them.
Just before he went unconscious, he realized he had not been careful, finally understanding his bad habit, he even thinks he deserves his death for his arrogant mistake. He gets scared at the idea of dying and makes one last attempt at getting back up, Nail crushes his chest in response, seemingly killing Recoome, but he survives barely, he's currently healing inside a healing tank.
The two last survivors
While Recoome and Burter enjoyed their lunch, several soldiers raced towards an unidentified ship, which slightly shocked the two. After Recoome hears about the intruders, he rushes towards Gokū and attacks him, while soldiers run in panic not wanting to get caught in Recoome's attacks. After a short battle between the two, Recoome is knocked out, Burter rushes in and punches Gokū in the gut. After Gokū knocks down Burter, Recoome grabs Gokū's foot and mocks him to not underestimate him. When Gokū asks the two the whereabouts of Freeza, Recoome mocks him again saying he'd never stand a chance against them if they were Freeza. Recoome along with Burter are subsequently brutally damaged by the two intruders. When Captain Ginyu arrives at the scene, Recoome reassures him that the both of them are alive, as Ginyu thought they were dead. Several minutes later, Recoome retrieves Ginyu in Nail's body. Nail attempts to masquerade as Ginyu, but Recoome doesn't fall for it and Ginyu switches bodies with Nail once again, leaving Nail to die from his wounds.