The most common and most likely answer to this crossword clue is the 8 letter word CANNIBAL
I've seen this crossword clue in The Sunday Telegraph
C
A
N
N
I
B
A
L
More clues leading to the result CANNIBAL
- One being given sustenance by another
- Nick writing tip by a liberal, one with unusual tastes
- Dangerous tribesperson makes writer dive into water
- Fellow consumer?
- One who would put away other people
- Cold Cockney man crossing the Alps, one eating what most of us wouldn’t!
- Unpleasant consumer channel retaining some point
- Writer’s piece screened by channel, might one finish another off?
- Cold girl — one starts to beguile all lovers as man-eater
- Might one have you for dinner?
Buddy explains!

The straight part
We know that "might one finish another off?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case might one finish another off? = cannibal.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CANNIBAL mean?
CANNIBAL noun- An organism which eats others of its own species or kind, especially a human who eats human flesh.