Song girl of questionable identity and status (6)

I believe the answer is:

sylvia

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'song girl' is the definition.
'Sylvia' can be an answer for 'girl'. I am not sure about the 'song' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for sylvia that I've seen before include "American poet, 1932-63" , "Girl's name" .)

I've seen this clue in The Globe and Mail.

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