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If X is inside something, what is that something's relationship to X?
The dog is inside the house.
→ The house is _ _ _ _ the dog.
I was thinking of around, but it really sounds ugly, and it hardly works when inside isn't a cavern of some sort ("I'm in the park, the park is around me").
There isn’t one, because we don’t need one. Around the dog or around me may or may not be ‘ugly’, but it just isn’t something anyone would say in that kind of context.
Barrie is right (in the contexts you describe) - but do you mean to say enclose?
