Housing - very steep housing - for subaltern (7)

I believe the answer is:

shelter

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'housing' is the definition.
(I know that shelter is a type of housing)

'steep housing for subaltern' is the wordplay.
'steep' becomes 'sheer' (similar in meaning).
'housing' indicates putting letters inside.
'for subaltern' becomes 'lt' (I can't explain this - if you can you should believe this answer much more).
'sheer' going around 'lt' is 'SHELTER'.

'very' is the link.

Can you help me to learn more?

(Other definitions for shelter that I've seen before include "retreat" , "Refuge or protective cover" , "Shield as from rain" , "Find refuge" , "Sanctuary, protection" .)

I've seen this clue in The Independent.

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