Crossword Genius

Where the dying go, we stay? Not half (4)

Ross

I believe the answer is:

west

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'where the dying' is the definition.
The answer is a location as well as being a singular noun. This is suggested by the definition.

'we stay? not half' is the wordplay.
'not half' suggests halving the letters.
'stay' with half the letters taken is 'st'.
'we'+'st'='WEST'

'go' is the link.

Can you help me to learn more?

(Other definitions for west that I've seen before include "Colombian with brews (anag)" , "Small white dog" , "English county" , "Occident" , "'Go ___ , young man'" .)

I've seen this clue in The Independent.
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