The most common and most likely answer to this crossword clue is the 4 plus 5 letter word ONLY HUMAN
I've seen this crossword clue in Financial Times
O
N
L
Y
H
U
M
A
N
More clues leading to the result ONLY HUMAN
Buddy explains!
The straight part
We know that "The last person on earth/to admit to his failings" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the last person on earth/to admit to his failings = only human.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.