The most common and most likely answer to this crossword clue is the 8 letter word MORIBUND
I've seen this crossword clue in Financial Times
M
O
R
I
B
U
N
D
More clues leading to the result MORIBUND
- Decaying bone found in knoll
- Dying to tease in bank?
- Bone in heap, not quite dead?
- Bone put in heap on the way out
- Dying to have a dig into bank
- Lifeless bank suppressing ridicule
- Bone put in pile on the way out
- Near death, bone found in heap
- Bone in tumulus showing indication of death
- Lifeless bone's buried in pile of earth
Buddy explains!

The straight part
We know that "on the way out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case on the way out = moribund.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 MORIBUND mean?
MORIBUND noun- A person who is near to dying.
- Approaching death; about to die; dying; expiring.
- Almost obsolete, nearing an end.