Basic Trope: A character trait becomes exaggerated over time.
Straight: Alice is a character on Alice and Bob: she's well-rounded, but her most defining trait is her political activism. In later seasons, all facets of her character are drowned out to where the political activism is all that remains of her characterization.
Every character on Alice and Bob slowly becomes a one-note character with only one hobby.
Alice goes from a basic character who occasionally mentions the president to a crazed political activist who yells at anyone who doesn't agree with her side.
The entire Alice and Bob series, originally a lighthearted political satire, soon ends up as a blatant piece of propaganda with Straw Characters built all over the place to attack various political, religious, and ethnic groups.
Alice becomes more and more interested in politics as time passes, but still has other traits.
Alice also starts appearing less.
The political activism is solely in retaliation to the creeping political plot lines in the story.
Alice's friends, seeing her talent in political activism, encouraged her to pursue it more and more, and Alice does just that.
Alice and Bob is a show focusing mainly on political satire, and the writers want to make Alice, who they use to comment on current events, to focus more and more on commenting on politics.
The work is a commentary on how Political Activism takes over peoples lives and makes them become more and more extreme
There are now Loads and Loads of Characters, and Alice's political activism is the main trait setting her apart from the rest of the characters and the only thing worth showing
Lampshaded: "Remember when you used to do other things than just protest all the time?" "Sounds like you're a victim of the liberal agenda, Bob."
Invoked: Alice decides that anything else in her life will just distract her from her main goal, and therefore focuses on political activism.
Exploited: Every time Bob wants to distract Alice, he just mentions politics.
Defied: Alice realizes that she's becoming obsessed and decides to stop talking about politics for a while.
Discussed: "Alice, I think you should see a therapist. Unlike what you see on TV, normal people don't become like this!"
Conversed: "You remember when the characters on this show used to behave like regular people? I guess the writers got lazy. Never mind, it's much more entertaining this way."
Implied: Alice is a minor or offscreen character, so we don't know for sure that her personality is changing.
This mischaracterization causes two things: first, the people who didn't define with Alice's political activism are now uninterested by her; second, the people who did enjoy Alice's political activism now find that it's being pushed down their throats. As a result, both groups stop watching.
In-universe example: Alice's co-star Bob gets fed up with Alice's obsession with political activism and laments the days when she had other traits as well.
Alice has a Freudian Excuse: she only became a radical pro-choice extremist when strict abortion laws in her country forced her to go to a Back-Alley Doctor to terminate her pregnancy, resulting in a severe infection and later a hysterectomy.
As a result of an Author's Saving Throw, Alice's old personality is revived and her popularity is reborn.
Alternatively: The new Flanderized character of Alice becomes incredibly popular since the trait that is now her only trait was the only trait that viewers remembered anyway, and they felt that her other traits only distracted from the brilliance of the dominant trait.
Alice explains to Bob that a vote on a particular issue she cares about is coming up, and since she's a member of a political activist group based on that issue, she can't stop thinking about it until the vote is over. Once that's done, she goes back to being a more nuanced person.
Played For Laughs: Alice's obsession in shown as something hilarious, and other characters always make jokes at her expense.
Played For Drama: Alice loses all of her friends who aren't interested in political activism.
You seem pretty interesting, but you just know that sooner or later your only defining trait will be that you want to go back to Flanderization.