The most common and most likely answer to this crossword clue is the 8 letter word OUTLIVED
I've seen this crossword clue in The Guardian
O
U
T
L
I
V
E
D
Buddy explains!

The straight part
We know that "went on longer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case went on longer = outlived.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 OUTLIVED mean?
OUTLIVED verb- To live longer than; continue to live after the death of; overlive; survive.
- To live through or past (a given time).
- To surpass in duration; outlast.
- To live longer; continue to live.