Feign endless embarrassment for one’s actions (4)
I believe the answer is:
sham
'feign' is the definition.
(both can mean to pretend)
'endless embarrassment for one's actions' is the wordplay.
'endless' means to remove the last letter.
'embarrassment for one's actions' becomes 'shame'.
'shame' with its final letter removed is 'SHAM'.
(Other definitions for sham that I've seen before include "Not what it seems to be" , "Pretense; bogus" , "Pretence; bogus, false" , "Pretence, hoax" , "Feign" .)