Torn piece of linen that can mean a clean sheet (3)

I believe the answer is:

nil

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'can mean a clean sheet' is the definition.
I can't tell whether this defines the answer.

'torn piece of linen' is the wordplay.
'torn' becomes 'ni' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'piece of' indicates taking the first letters.
The first letter of 'linen' is 'l'.
'ni'+'l'='NIL'

'that' is the link.

Can you help me to learn more?

(Other definitions for nil that I've seen before include "Nothing, no score" , "There's nothing left" , "Zero, zilch" , "0" , "Lacking value" .)

I've seen this clue in the Evening Standard.

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