Alternatively, Bob decides he can do better than Alice or Claire, so he goes to find himself a new girlfriend.
Or, each girl attempts to repeatedly kill each other. Bonus points if they're doing this with a ship motif in there. When each character is about to bite the big one, Bob comes in and saves her. Make sure you hint that this happens repeatedly and daily...or hourly.
Zig Zagged: In canon, Alice and Bob are together and Claire and Dennis are together. In fanon, they're all together.
A fanfic writer simply pairs up Bob and Alice, without killing or derailing Claire.
Enforced: Bob tells Claire in no uncertain terms that he loves Alice.
Lampshaded: "Ain't it strange that there is always a characters hated by the fans because they're a threat to the characters they ship?"
Invoked: "That whore! She's trying to take Bob away from Claire! I'll write a fanfic about this and she will PAY!"
"You know what? If Bob prefers Claire over Alice, that's fine with me".
Bob dies, or Alice and Claire both die, or just one of them dies but both ships sink with them.
Fans simply resolve the issue by shipping Alice with someone else.
Discussed: "What makes Alice better than Claire, I 'd like to know?"
Conversed: "You know, instead of killing off Claire like most fanfic writers do, you could always have her just want Bob to be happy".
After Claire dies, Bob gets with Alice in an attempt to move on from her. It's a bit of a rash move though. He's still grieving for Claire, and the relationship suffers and ends quickly because of this.
The writer decides to go with a Die for Our Ship, but twists it, causing the plot to get derailed due to screwing with several characters' personalities. This results in the entire fan-base going against the original shippers for causing a Romantic Plot Tumor.
Plotted A Good Waste: Creators don't like one of their characters anymore so they intentionally pair her up so that she'll be hated by the fans. Then she can be killed off easily without much protest by fans.