Failing to find family in Chinese dynasty (7)

I believe the answer is:

tanking

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'failing' is the definition.
The answer and definition can be both related to change as well as being present participle verbs.
Perhaps you can see a link between them that I can't see?

'family in chinese dynasty' is the wordplay.
'family' becomes 'kin' (synonyms).
'in' is an insertion indicator.
'chinese dynasty' becomes 'tang' (I've seen this before).
'kin' inserted within 'tang' is 'TANKING'.

'to find' is the link.

Can you help me to learn more?

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

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