Dog's den free — a stroke of good luck (7)

I believe the answer is:

godsend

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'a stroke of good luck' is the definition.
I can't tell whether this defines the answer.

'dog's den free' is the wordplay.
'free' indicates anagramming the letters.
'dogs'+'den'='dogsden'
'dogsden' with letters rearranged gives 'GODSEND'.

Can you help me to learn more?

(Other definitions for godsend that I've seen before include "Very welcome thing" , "Lucky find" , "welcome acquisition" , "The relief" , "Something very opportune" .)

I've seen this clue in The Times.

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