To resign, in any case, means pain (5)
I believe the answer is:
agony
'pain' is the definition.
(agony is a kind of pain)
'to resign in any case' is the wordplay.
'to resign' becomes 'gon' (I can't justify this - if you can you should believe this answer much more).
'in' means one lot of letters goes inside another.
'case' says to hollow out the word (remove centre letters).
'any' with its centre taken out is 'ay'.
'gon' put into 'ay' is 'AGONY'.
'means' is the link.
Can you help me to learn more?
(Other definitions for agony that I've seen before include "Severe pain, mental or physical" , "Extreme pain" , "Really severe pain" , "Extreme suffering - kind of aunt" , "Distress" .)