Sort of stone sink (4)

I believe the answer is:

flag

I believe this is a double definition.

'sort of stone' is the first definition.

'sink' is the second definition.
(flagging is a kind of sinking)

(Other definitions for flag that I've seen before include "Droop with tiredness" , "Give a signal" , "National standard" , "fade" , "Symbol or emblem of a country" .)

I've seen this clue in The Telegraph.

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