The 84-year-old was found with her 87-year-old husband at their home in Overend Road, in Cradley, at around 8.55am on Monday.
Ambulance crews were called to the scene, described as a "medical emergency", with the couple both in a critical condition.
They were taken to Russells Hall Hospital before the man died on Wednesday.
West Midlands Police has now confirmed that the woman is in a "serious but stable condition" in hospital.
A police investigation is still ongoing, and they were unable to confirm whether it is a criminal investigation.