The most common and most likely answer to this crossword clue is the 4 plus 4 letter word LAST LEGS
L
A
S
T
L
E
G
S
Buddy explains!
The straight part
We know that "on them? You’re nearly finished!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case on them? you’re nearly finished! = last legs.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.