It's my fault. I had to kill so many other people's children...but I kept you alive because you were my daughter. I had no right to be so selfish. It was my sin from the beginning, but you'll have to pay.
–Kurama, finding this weapon never more powerful than when he puts it aside to embrace his child
The pistol ends up becoming a bit symbolic as the series closes. Kurama, at first seemingly hell-bent on killing his out-of-control Diclonius daughter Mariko. Instead, he drops it, partly at the urging of Nana, instead embracing his child and letting her know that her father loved her and her mother sacrificed her life to save her. Finally, the discarded gun is all that is left of the Kuramas after Doctor Kurama chooses to die when Mariko's embedded bombs finally go off.
Unknown Pistol In The Manga
In the manga's version of the Mariko arc, Kurama plans to execute Mariko when she is in her helpless infantile state but is stopped by Nana. He then tries to kill Nyu to stymie Chief Kakuzawa's schemes, but only succeeds in awakening Lucy.
In the manga's final story arc, Kurama carries a pistol with which he reluctantly kills Mariko's clone Barbara to save Nana's life, simultaneously accepting that Mariko is gone and fulfilling a sick desire on the part of Chief Kakuzawa to have him kill Mariko (or at least as Kurama speculates). Kurama finally attempts to murder Lucy by shooting her, only to have Kouta step in the way of the bullet, putting him at death's door and enraging Lucy so, she chose to try and end the world before deciding instead to heal him. It is possible to speculate whether these are all one gun in the manga, although impossible to prove with any accuracy.