Did you notice that ミラーさん is marked with the subject marker (が) rather than the topic marker (は)? This means ミラーさん is the subject of the relative clause that modifies うち (I'm assuming you know the basics of relative clauses). And this usually also suggests that the subjects of かいました and すんでいた are different! If the subjects of the two verbs were the same, the sentence would have been written using は, with ミラーさん as the topic of the entire sentence, like this:
ミラーさんはすんでいたうちをかいました。
Mira-san purchased the house where he lived.
The structure of your sentence, however, suggests that ミラーさん is the subject of only すんでいた. The subject of かいました is not explicitly specified at all, but we can assume it's someone other than Mira-san.
ミラーさんがすんでいたうちをかいました。
[I/he/she/you/we] purchased the house where Mira-san lived.
EDIT: Note that が can still mark the subject of the entire sentence if the sentence is a special sentence called a 現象文. But this isn't a likely interpretation at least in this specific case.