If a vampire had approached her three years ago and asked her to run away with him, she would have said no in a heartbeat. She had a life in Mystic Falls. She had a mom and a dad and a loser littler brother and she loved it there. She had no reason to even think about running.
Now, when Damon presents the option, it seems like not just a good choice, but the only one. Every reason she had to stay was gone. Her parents were dead. Aunt Jenna was dead. Her biological mother and father were dead. Alaric was dead. Stefan was dead. Her best friend had been turned in to a Vampire, and more recently, been brutally killed by her other best friend, who had gone darkside and started killing, well,everyone.
Elena Gilbert's life, as of late, had been a little hectic.
There were only two things left in the world that Elena cared about, number one was Jeremy. If he and Tyler hadn't already left town (hopefully they were halfway around the world by now), Elena wouldn't even consider leaving. Number two was standing in front of her, asking her to run away.
After what felt like hours, but was really only a minute or two, she finally answered.