Liz Forbes dies in the fight to kill Klaus. She was firmly on Caroline's side in the end and no one else's. She didn't give a damn if any of the other vampires survived the fight, but what it had come down to was that Caroline was her daughter and she wasn't going to let her die (again) at the hands of some really old vampire.
She protected Caroline as much as she possibly could, but human limitations were her downfall in the end, and Damon would have been the first to have admitted to predicting that outcome.
All the remaining members of their little gang of supernatural misfits show up at the funeral, if only to support Caroline. And everyone's surprised when Katherine shows up as well—hiding in the shadows as to not be seen by the human attendees.
And afterward, when Caroline's back at the boarding house (where everyone is staying because no one wants to be truly alone after all they've gone through), Caroline breaks down in the living room, and Elena, Bonnie, Tyler, and even Damon try comforting her. When nothing works, they make for the kitchen and attempt to leave her alone.
She's not alone for long when Katherine makes her entrance—loud and showy—and sits herself on the floor next to where Caroline had fallen.
"He killed my mother too," she whispers.
Caroline stops crying at the words and sniffles as she lifts her head to stare at the vampire double of her best friend.
Katherine's hand is hesitant and surprisingly gentle as she reaches out and fixes the blonde's hair and wipes at her tears. Caroline closes her eyes and, for some reason, is reminded of the way her mother used to do almost the same thing when Caroline would come home from school upset over something.
"He killed everyone I loved—everyone I knew," Katherine continues. "But you still have people who you love. You still have Elena and Bonnie and Tyler. and, hell…sometimes I think there may be a part of Damon that cares about you. Even I don't mind having you around, I suppose. You're feisty—I like that."
Hearing that it could have been much worse (that she could have been the last one standing) makes her realize that maybe she'll be alright.
And as Katherine gets up and leaves her on the floor again, Caroline watches her heels click across the floor with the hint of a smile on her face.