。
She lives all alone in an absurdly big house.
Literal
She [topic-は] preposterously big house [in-に] alone is-living.
とてつもなく ('preposterously, extraordinarily, beyond reason') is the adverbial form of the i-adjective とてつもない, used to crank an attribute past expectation — bigger than any reasonable house should be. The 一人で here doubles down on the solitude framing already implied by the oversized house, with hint of being unable to fill it. ~ている marks the long-term state of dwelling.