Chest bone found in tumulus near the end (8)
I believe the answer is:
moribund
'near the end' is the definition.
'chest bone found in tumulus' is the wordplay.
'chest bone' becomes 'rib' (I've seen this before).
'found in' indicates putting letters inside.
'tumulus' becomes 'mound'.
'rib' inserted inside 'mound' is 'MORIBUND'.
(Other definitions for moribund that I've seen before include "In terminal decline" , "Decaying" , "At death's door" , "Stagnant - dying" , "Lifeless" .)