In a nutshell, one who is unlikely to change (4,4)
I believe the answer is:
hard case
If this is the answer, I'm afraid I cannot explain it.
Can you help me to learn more?
(Other definitions for hard case that I've seen before include "challenge to legal team?" , "Tough person to deal with" , "Tough guy" , "Brief problem, perhaps" , "Intractable person" .)