Answer:
"Theirs" in used in the "genitive case".
Step-by-step explanation:
In the sentence provided, "theirs" functions as a possessive pronoun replacing the noun phrase "their house".
The genitive case is a grammatical one that expresses possession, generally, by adding an apostrophe followed by "s".
The genitive case is also known as "the Saxon genitive" since it comes from the old English which left its mark ('s endings) in modern English.