No sis, it's not allowed to kill under such circumstances. As muslims we believe that the suffering of illness wipes away our sins. We should remind that person of this and also of the torture of the grave and jahanum which they may be saved from due to their present suffering. Even the extreme kind of suffering in this world will seem like a blessing compared to the tortures of the hereafter.

I'm certain it's haram but will bring daleel inshaAllah