This is kind of a theory. Mostly, it's based on when you kill Sans, he says "Papyrus, do you want anything?" because he is hallucinating. i think somehow Papyrus "came back", and found the player and Sans. Because Sans is dying, he doesn't remember Papyrus is dead, so if Papyrus came back or Sans hallucinated, he isn't like "Papyrus, weren't you dead?". it kind of hints at Papyrus coming back because when he dies he tells you he still believes in you, and usually hints like that mean something will stop him believing in you and something will happen. As you keep killing, Papyrus loses more belief, and has none for you when you kill Sans. The reason he doesn't start a battle for killing his brother like Sans did is that he knows he has weak attacks. Then he probably watches you continue, as you kill Asgore and Flowey. i don't know how Papyrus would come back, but he's a skeleton, and you cut his head off, how does that kill him? He doesn't even have muscles to move, so pulling his skull off should be harmless. And he talks for a minute while decapitated. He does disintegrate, but the interesting this is his soul doesn't crack in 2. So maybe it persisted because he still believed in you, he was determined. And maybe, if there is an "Undertale 2" or something, he will come back, and he will be as powerful as Sans.