The key to all this IMO is that Alex is the monster. And that Chloe couldn't reply on any of her circle for help.
Becky and Chloe were very close friends at school. Chloe moved schools and started seeing Alex.
Alex is - and always was - a possessive, jealous, dangerous man (or boy). We know that from the letter Becky finds, that Chloe wrote to her, but tells her Alex doesn't want her to send it. She was already afraid of him at that point, but like many sociopaths, he was charming and loved by others so she doubted herself. Alex was probably jealous of their friendship and wanted rid of Becky.
Chloe plotted to leave Alex with Richard. When he found out, she was terrified. She tried to tell Liv at the hotel (Liv wouldn't listen, on the CCTV), then she went outside expecting Richard to be there as arranged, but he had let her down too. So she fled to her parents, but even they let her down, falling for his bullshit instead of protecting their daughter.
So, when she ended up drugged and terrified on the the edge of a cliff, trying to escape Alex, she called the only person she could think of who she could trust to help get, and not be sucked in by Alex - Becky.
That's what makes sense to me, anyway!