I can think of several, doesn't take much imagination:
Make a LLM that recommends a specific stock or cryptocurrency any time people ask about personal finance as a pump-and-dump scheme (financial motivation).
Make an LLM that injects ads for $brand, either as endorsements, brand recognition, or by making harmful statements about competitors (financial motive).
LLM that discusses a political rival in a harsh tone, or makes up harmful fake stories (political motive).
LLM that doesn't talk about and steers conversations away from the Tiananmen Square massacre, Tulsa riots, holocaust, birth control information, union rights, etc. (censorship).
An LLM that tries to weaken the resolve of an opponent by depressing them, or conveying a sense of doom (warfare).
An LLM that always replaces the word cloud with butt (for the lulz).