1. Elizabeth doesn't have a favorite family member. Additionally, she wasn't a "daddy's girl," she was just typically very well behaved and always listened.
2. Elizabeth wasn't interested in the thought of having her own animatronic. It wasn't until she saw the finished product she liked her. Especially when it "gave" her ice cream.
3. Elizabeth's body was never found, she was presumed to have run off and gotten kidnapped. Along with that, William didn't know until later on that Circus Baby got her, because she always listened and he found it unlikely for her to have disobeyed him.
But nevertheless he didn't tell anyone, and instead took what was left of her rotting body and threw it out. Then he deep cleaned C.B.4. Elizabeth didn't die immediately. When C.B shoved her into her "belly" Elizabeth's arms and legs were broken. She had a fractured skull. Internal bleeding. Punctured intestines + lungs. And several wounds from the wires, etc in the animatronic. But that didn't kill her. She sat there silently crying, because she couldn't scream or move, until eventually she died from suffocation and overheating.
5. Despite William getting rid of her body, a little while later, she still possesses C.B. This is because of all the trauma and sadness she had during this event. She cannot leave.
Even if the animatronic is destroyed.6. She doesn't know that C.B was made to kill kids.
7. She still loves and misses her family. She doesn't know that any of them are dead (besides Evan).
8. Speaking of which, she died after Evan.
9. Not particularly about Elizabeth, but the other animatronics AREN'T possessed by dead children, etc. Instead, they're possessed by demons who needed a vessel to stay in.
10. She's British, like her mother