Crossword Genius

Finished with depression consuming the heart (7)

Ross

I believe the answer is:

through

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'finished' is the definition.
(similar in meaning)

'depression consuming the heart' is the wordplay.
I cannot quite see how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found within the answer.
'heart' could be 'h' (card game abbreviation) and 'h' is present in the answer.
The remaining letters 'rough' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

'with' is the link.

Can you help me to learn more?

(Other definitions for through that I've seen before include "As a result of" , "From beginning to end" , "Per" , "Non-stop - finished" , "made it to the next stage" .)

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