Weeps because huts lead to a rent (5,1,4)

I believe the answer is:

sheds a tear

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'weeps because' is the definition.
I know nothing about this answer so I can't judge whether it can be defined by this definition.

'huts lead to a rent' is the wordplay.
'huts' becomes 'sheds' (I've seen this before).
'lead' means one lot of letters go next to another.
'rent' becomes 'tear' (synonyms).
'sheds'+'a'+'tear'='SHEDS A TEAR'

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I've seen this clue in the Sydney Morning Herald.

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