She is in a very dangerous condition.

Literal

She [topic-は] very dangerous condition [in-に] exists.

状態にある ('exists in a state of') is a stiff, formal way of saying 'is in [some state]' — favored in news, medical reports, and academic prose where the casual ~の状態だ would feel too informal. ある here is the existential verb 'exist,' not the copula, so the locative に carries real meaning: 'exists at/in.'