To pad the story to movie length...

I think they just have to convince those kids, both about they being kind (wouldn't hurt them) and the reason to go with them being trustworthy. They do this by basically saying "the world is going to end, you can come with us and we'll take care of you. If you don't believe me, I can tell you this: there will be this disaster and this disaster and many to follow, and then there is THE END, you can check the news tomorrow - or as long as you need, just make up your mind before the last one come". So Lucinda said "they whisper scary things to her", and when she grew up she verified their predictions numerous times. But she eventually refuse to go with them, I think it's about "EE" (she wrote "EVERYONE ELSE") - maybe she never met another chosen one that's close enough, and for a kid at her age it's much hard to choose to live alone with everyone else being dead. They've chosen her multiple times (she had 5 or 6 those rocks in her bedroom), but eventually she got married and gave birth to her daughter and I think those "tickets" expires, since "they" only take children, not adults.