It is possible for Cheyenne to die during the tutorial quest, in which case Sunny's dialogue will change slightly to show her remorse. It does not, however, have any real impact on the completion of the quest. It is also possible for her to die when fighting the geckos during the quest "Back in the Saddle". This also seems to prevent saving the town in "Ghost Town Gunfight" quest.
pc There is a game glitch that might cause Sunny Smiles to walk up to you and start a conversation. She gets stuck in an infinite loop and some seconds after the end of each conversation, she will try to talk to you again. [verified]