“Benighted” is a state of pitiful intellectual or moral ignorance. It generally comes from one’s lack of opportunity. It can also signify that something has been overtaken by darkness or ignorance.
The noun “sigh” is an interesting word choice here because of its connotations. A “sigh” generally signals dejection, weariness, longing, pain, or relief. If this subject is on her deathbed, one might expect to hear groans, coughs, breaths, etc. In characterizing the sounds coming from her subject as a “sigh,” the speaker suggests that the subject is longing for death and weary of her situation.