You can wrap things: a present but can you wrap somebody. Can you wrap somebody with your warmth? Does this make any sense to you? I obviously mean in a figurative way.
Normally you can only wrap Something up not people though the expression you have used sounds poetic.
You can wrap yourself up in warm clothes.
You can wrap someone around your little finger. (idiom)
hi maj for the meaning to wrap it mean cover you can cover present. meybe you can cover somebody with you kind and help
i hope i got it and understand what do you mean
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 Woodward's reply was promoted to an answer.
The second example sounds weird, doesn't it? I am trying to figure out how that could be done but it is really hard to imagine. Can you further explain?
To wrap someone around your (little) finger is an expression that means....
to persuade or get someone to do anything you want, to have them 'under your control'
Sometimes people say 'twist someone around your little finger'.
e.g. She has always been able to twist her boyfriend around her little finger.
= get him to do the things that she wants.
'Wrap' can usually replace 'twist'
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