The house on the street that is well-known in the locality has been renovated recently.
"That" here refers to "The house".
If it refers to "the street" then what's the use of mentioning the house. I hope this is clear.
Is there any rule which says that the word 'that' used after a prepostional phrase ( in the given example - "on the street") should ignore the noun of the prepositional phrase ("street") and instead refer to the subject of the sentence ("house")?
Absolutely NO. There's no such a rule.
eg: The man in the house that was built in 1909 was rather shabby.
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